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Description
So you want to know more about dog genetics, but no clue where to start? Well hopefully this guide can help explain what a genotype means and how the letters all work together to result in some nifty colors and patterns!
Most of the information here is adapted from doggenetics.co.uk or from this study at the University of Saskatchewan , with some help from other genetic gurus and my own interpretations! Image credits can be found on their individual sta.sh pages!
This journal has been mostly crafted for DARPG users, but anybody is welcome to bookmark it for reference!

This "part one" guide to canine genetics will hopefully help to explain how each allele changes the color of a dog's coat. For starters, let's do a little vocab from high school biology.

Genetics: The study of heredity and variations of inherited characteristics of an organism.
Gene: Information about a trait.
Allele: Each different type, or form, of a gene.
Genotype: A list of the alleles that make up the phenotype.
Phenotype: The physical characteristics of an organism, as determined by the genotype.
Homozygous: Alleles (usually one paternal and one maternal) are identical. Ex. HH, DD, AyAy
Heterozygous: Alleles are not identical. Ex. Hh, Dd, Ayat
Dominant: The allele that is physically expressed.
Recessive: The allele that is not physically expressed, but carried to offspring.
Eumelanin: Causes black, liver, blue, and isabella melanin (or pigment cell) on a dog's coat. Dominant to pheomelanin.
Pheomelanin: Causes varying shades of red/tan/cream melanin (or pigment cell) on a dog's coat. Recessive to eumelanin.

To see how different genes can interact, please see this guide: Guide to Canine Genetics II
Some interactions have been included below because the entire gene is dependent on another, not just an allele. (See the Agouti section for example)

Officially Mapped AllelesThe following alleles have been ordered in the hierarchy of genes that impact the phenotype. For example, the recessive red gene (ee) "replaces" the black/liver/blue/isabella hairs on a dog's coat, so the E allele has been listed first. More information can be found beneath each set of genes!

Extension: Em, Eg, Eh, E, eEm>Eg/Eh>E>eEm plus anything = the dog will be some shade of red/fawn/tan with a eumelanin (black, liver, blue, or isabella) mask.
EgE or Ege = *certain sighthound breeds only! the dog will show "grizzle" or "domino" markings; works similar to sable but the dog cannot have a mask in addition to the sable and the dog must also have ata or atat for it to show; if the dog has any other A gene, that will show instead.
EhE or Ehe = *Cocker Spaniels only! the dog will show grizzle/creeping tan-like markings that overrides dominant black.
EE or Ee = nothing happens, this gene will have no effect on the dog's physical traits.
ee = shows red and no other black markings (can have white spots or ticking), but the dog's skin color will still be determined by the eumelanin pigment (the B/D/K alleles). Known as "recessive red."

*Extension alleles (except for ee) will only show if the dog has recessive kk black that allows tan or red areas to show. A dog with "ee" will show red regardless of the K allele.
*The E allele will override the K allele; even if a dog is solid black (K_), but has Em_, it will display some shade of red with a mask; if it is K_ and has e_, it will display a solid shade of red. Only when the E allele is E_ will the K allele be revealed (and even then, it can be hidden under the colors listed above).

Red intensity: C, cch, ceC>cch>ceC plus anything = red
cchcch, cchce = red turns to cream/tan (sometimes called lemon)
cece = red turns to silver/near white (often called platinum)

*this gene is technically still theoretical, but is common in DARPG to explain the varying shades of red dogs! In other theories and studies, the C allele is associated with the gene SLC45A2, thought to be responsible for albinism in Dobermans and small breeds of dogs. Check out this article for more research on the correlation between the C and E alleles and albinism!

Liver (brown, aka chocolate): B, bB>bB plus anything = "regular" color, not liver
Bb = "regular" color, carries liver to pups if bred to another Bb or bb dog
bb = the dog's base coat color will be liver

*There is an exception when it comes to 'red' dogs, seen below under the C and I loci. If a dog has recessive red (ee), even though eumelanin pigment (the B/D/K alleles) may also be present, then the dog will look red as opposed to black/liver/blue/isabella. However, the dog's skin color will still be determined by the eumelanin pigment (the B/D/K alleles). This may be referred to as dilute factored red.

Blue (dilute, aka slate/steel): D, dD>dD plus anything = "regular" color, not blue
Dd = "regular" color, carries blue to pups if bred to another Dd or dd dog
dd = the dog's base coat color will be blue

*There is an exception when it comes to 'red' dogs, seen below under the C and I loci. If a dog has recessive red (ee), even though eumelanin pigment (the B/D/K alleles) may also be present, then the dog will look red as opposed to black/liver/blue/isabella. However, the dog's skin color will still be determined by the eumelanin pigment (the B/D/K alleles). This may be referred to as dilute factored red.

Isabella (aka lilac/silver grey): bb ddIf the dog has BOTH bb and dd, it is isabella colored, which is also referred to as a "double dilute" occasionally, because both dilute genes are present and have an effect on the resulting physical coat color of the dog.

Black/brindle: K, Kbr, kK>Kbr>kK plus anything = "regular" color, no tan markings; generally black unless liver, blue, isabella, merle, and/or greying is present*
KbrKbr or Kbrk = brindle tan over base color
kk = the dog will show any tan marking or possibly a varying shade of red

*The dominant K allele overrides all other color genes except for liver, blue, merle, and greying. If a dog has bb, dd, and/or Mm (even if the dog also has KK, KbrKbr, Kk, or Kbrk), the dilute, merle, and greying genes will override a black dog. Greying can also affect black coats (see the G allele below).
*The E allele will override the K allele; even if a dog is solid black (K_), but has Em_, it will display some shade of red with a mask; if it is K_ and has e_, it will display a solid shade of red. Only when the E allele is E_ will the K allele be revealed (and even then, it can be hidden under the colors listed above).
*Brindle varies in thickness/coverage, and has not been proven to be the effect of any other gene.
*There is an exception when it comes to 'red' dogs, seen above/below under the C and I alleles. If a dog has recessive red (ee), even though eumelanin pigment (the B/D/K alleles) may also be present, then the dog will look red as opposed to black/liver/blue/isabella. However, the dog's skin color will still be determined by the eumelanin pigment (the B/D/K alleles). This may be referred to as dilute factored red.
*note that the examples below are all black with tan points; the black can be replaced with liver, blue, isabella, or merle if the proper gene is present

Agouti: Ay, aw, at, aAy>aw>at>aAy plus anything = fawn (ranging from golden to cream) or sable* (ranging in intensity from lots of black to hardly any, called "clear")
awaw, awat, awa = agouti, aka "wolf agouti" or "wild"; note that "sable" GSDs are often agouti and not genetically Ay, but aw.
atat, ata = saddle/creeping tan/tan points*
aa = recessive "regular" color (often referred to as recessive black); even if the dog is kk which allows tan markings to show, if it has aa, it will appear solid and the base color will be determined by the B/D/K alleles.

*sable can be "tipped" or "shaded", as seen from the examples below
*saddle/creeping tan/tan points is only expressed if the dog also has kk and either Em or E in the genes; otherwise, it will either be black, brindle, or recessive red, and the saddle/tan genes will carry to offspring but will not show in the dog's phenotype. See here for official information.
If you use genetics in DARPG to determine between saddle or tan points, you'd first have to determine if both of those markings are possible in the breed, and if so, RNG to see whether one of those genes also contains the RALY (saddle) gene or not; YES=saddle, NO=tan points. If only one of the markings shows up in the breed, then atat and ata will only show that one marking (ie. Dobermans only have tan points and Beagles only have saddles).
*creeping tan refers to a pattern that looks like a mix of tan points and saddle; the tan reaches farther on the dog's body (covers most of the face, legs, and reaches to the chest) than traditional tan points, but does not recede far enough to be distinguished as saddle. Progression of creeping tan with age can be found here.
*note that the examples below are all black with tan points; the black can be replaced with liver, blue, isabella, or merle if the proper gene is present

Merle: M, mM>mMM = double merle
Mm = merle
mm = no merle
**Ma = atypical merle
**Mc = cryptic merle

*merle is merely a "pattern overlay" on eumelanin pigment. This means that merle only shows on genetically black, blue, liver, or isabella dogs. It would be "hidden" on a red dog (sometimes you can tell that if a red dog has blue eyes, it likely has hidden, or "phantom", merle).
*a blue merle would genetically be dd Mm and a red merle would actually be a liver merle, bb Mm.
*breeding merle is often very dangerous, as double merle dogs are almost always born with problems, or can even be stillborn! It's a highly discouraged practice; you should always breed a merle dog to a non-merle dog!
**only proven in Catahoula Leopard Dogs and Dachshunds thus far, Ma and Mc are extensions of the merle gene that also affect whether or not a dog physically displays merle, or how it is displayed. More information can be found here.

Harlequin: H, hHH = lethal
Hh = harlequin
hh = no harlequin

*harlequin is a unique gene that does not display on its own. It requires the presence of merle (Mm or MM) to show. If a dog has the Harlequin gene, but is mm, meaning it doesn't have merle, it only carries harlequin until bred to a merle.
*harlequin acts the same way that merle does in the fact that it only affects eumelanin pigmented dogs.
See the Guide to Canine Genetics II for examples of how Merle and Harlequin interact.

White (spotting): S, si, sp, sw
S>si>sp>swS plus anything = the dog will be solid; occasionally a genetically solid dog may have "residual/minimal" white (such as a small star on the chest or white toes), which is not genetic!
sisi, sisp, sisw = irish white; can be collared or not
spsp, spsw = piebald white
swsw = extreme piebald white

*the si and sw genes are technically still theoretical, but are common in DARPG to explain the varying amount of white on a dog!
*extreme piebald may also be referred to as "hooded" in certain breeds when the white covers everywhere except the head and occasionally a patch on the rump.
*some believe that irregular white markings on a dog's face is a result of irish and piebald (sisp/sisw) or a combination of (hidden) merle, but this has not been proven.

Ticking/roaning: T, tr, t
T>tr>t
T plus anything = ticking (heavier density)
Tt = ticking (lighter density)
trtr or trt = roaning
tt = clear white (no ticking)

*roaning is technically still theoretical, but commonly used to refer to the spotting of breeds like the Australian Cattle Dog or German Shorthair Pointer!
*ticking can sometimes be referred to as "belton", especially in sporting dogs!

Additional Genetic Notes (theoretical alleles)
All of the above alleles have been proven to exist in some form or fashion, but there are a few additional genes that are not technically confirmed but are suspected to have an effect on a dog's coat color or patterns.

Intensity: I, iII = red coat color will appear somewhat "bleached" from its namesake (ie. red may be closer to orange or cream); predicted to be responsible for creating "white" dogs who don't show other colors with white patterns, like Samoyeds
Ii = intensity has minimal effect on the dog's red coat color (ie. a deep mahogany red will appear more crimson)
ii = intensity has no effect on the dog's red coat color (a red dog will appear its original rich red)

*this gene is theorized to take place of the C allele above to control red intensity, according to the study from the University of Saskatchewan; in that study, the C allele instead theorizes a gene that causes albinism in some breeds.
*the intensity gene is only suspected to have an effect on pheomelanin (aka dogs who present some shade of red in their coat); does not affect eumelanin coats.
*intensity may develop over time, lightening the coat of a dog who was born with a darker shade.

Greying: G, gGG = light grey develops over time
Gg = medium grey coat develops over time
gg = dark grey coat develops over time, or no greying at all

*any dog may possess the greying gene but some breeds show it better than others; what it does is lighten the black pigment of the dog as the dog ages. In some cases, greying may only affect the muzzle area and give the dog a greyed mask even if it had no mask before.

Tweed: Tw, twTwTw: tweed
Twtw: "regular" color, carries tweed to pups if bred to another TwTw or Twtw dog
twtw: no tweed

*tweed refers to the appearance of multiple colors of merle patches, as opposed to a few "dilute" patches that may be seen in normal merles.

Urajiro: U, uUU = urajiro
Uu = "regular" color, carries urajiro to pups if bred to another Uu or uu dog
uu = no urajiro

*urajiro refers to the lightening of pigment in some breeds of dogs in the general area that tan points and/or irish white and/or agouti would change the pigment, but is suspected to be a gene unto itself.

Description
So you want to know more about dog genetics, but no clue where to start? Well hopefully this guide can help explain what a genotype means and how the letters all work together to result in some nifty colors and patterns!
Most of the information here is adapted from doggenetics.co.uk or from this study at the University of Saskatchewan , with some help from other genetic gurus and my own interpretations! Image credits can be found on their individual sta.sh pages!
This journal has been mostly crafted for DARPG users, but anybody is welcome to bookmark it for reference!

This "part one" guide to canine genetics will hopefully help to explain how each allele changes the color of a dog's coat. For starters, let's do a little vocab from high school biology.

Genetics: The study of heredity and variations of inherited characteristics of an organism.
Gene: Information about a trait.
Allele: Each different type, or form, of a gene.
Genotype: A list of the alleles that make up the phenotype.
Phenotype: The physical characteristics of an organism, as determined by the genotype.
Homozygous: Alleles (usually one paternal and one maternal) are identical. Ex. HH, DD, AyAy
Heterozygous: Alleles are not identical. Ex. Hh, Dd, Ayat
Dominant: The allele that is physically expressed.
Recessive: The allele that is not physically expressed, but carried to offspring.
Eumelanin: Causes black, liver, blue, and isabella melanin (or pigment cell) on a dog's coat. Dominant to pheomelanin.
Pheomelanin: Causes varying shades of red/tan/cream melanin (or pigment cell) on a dog's coat. Recessive to eumelanin.

To see how different genes can interact, please see this guide: Guide to Canine Genetics II
Some interactions have been included below because the entire gene is dependent on another, not just an allele. (See the Agouti section for example)

Officially Mapped AllelesThe following alleles have been ordered in the hierarchy of genes that impact the phenotype. For example, the recessive red gene (ee) "replaces" the black/liver/blue/isabella hairs on a dog's coat, so the E allele has been listed first. More information can be found beneath each set of genes!

Extension: Em, Eg, Eh, E, eEm>Eg/Eh>E>eEm plus anything = the dog will be some shade of red/fawn/tan with a eumelanin (black, liver, blue, or isabella) mask.
EgE or Ege = *certain sighthound breeds only! the dog will show "grizzle" or "domino" markings; works similar to sable but the dog cannot have a mask in addition to the sable and the dog must also have ata or atat for it to show; if the dog has any other A gene, that will show instead.
EhE or Ehe = *Cocker Spaniels only! the dog will show grizzle/creeping tan-like markings that overrides dominant black.
EE or Ee = nothing happens, this gene will have no effect on the dog's physical traits.
ee = shows red and no other black markings (can have white spots or ticking), but the dog's skin color will still be determined by the eumelanin pigment (the B/D/K alleles). Known as "recessive red."

*Extension alleles (except for ee) will only show if the dog has recessive kk black that allows tan or red areas to show. A dog with "ee" will show red regardless of the K allele.
*The E allele will override the K allele; even if a dog is solid black (K_), but has Em_, it will display some shade of red with a mask; if it is K_ and has e_, it will display a solid shade of red. Only when the E allele is E_ will the K allele be revealed (and even then, it can be hidden under the colors listed above).

Red intensity: C, cch, ceC>cch>ceC plus anything = red
cchcch, cchce = red turns to cream/tan (sometimes called lemon)
cece = red turns to silver/near white (often called platinum)

*this gene is technically still theoretical, but is common in DARPG to explain the varying shades of red dogs! In other theories and studies, the C allele is associated with the gene SLC45A2, thought to be responsible for albinism in Dobermans and small breeds of dogs. Check out this article for more research on the correlation between the C and E alleles and albinism!

Liver (brown, aka chocolate): B, bB>bB plus anything = "regular" color, not liver
Bb = "regular" color, carries liver to pups if bred to another Bb or bb dog
bb = the dog's base coat color will be liver

*There is an exception when it comes to 'red' dogs, seen below under the C and I loci. If a dog has recessive red (ee), even though eumelanin pigment (the B/D/K alleles) may also be present, then the dog will look red as opposed to black/liver/blue/isabella. However, the dog's skin color will still be determined by the eumelanin pigment (the B/D/K alleles). This may be referred to as dilute factored red.

Blue (dilute, aka slate/steel): D, dD>dD plus anything = "regular" color, not blue
Dd = "regular" color, carries blue to pups if bred to another Dd or dd dog
dd = the dog's base coat color will be blue

*There is an exception when it comes to 'red' dogs, seen below under the C and I loci. If a dog has recessive red (ee), even though eumelanin pigment (the B/D/K alleles) may also be present, then the dog will look red as opposed to black/liver/blue/isabella. However, the dog's skin color will still be determined by the eumelanin pigment (the B/D/K alleles). This may be referred to as dilute factored red.

Isabella (aka lilac/silver grey): bb ddIf the dog has BOTH bb and dd, it is isabella colored, which is also referred to as a "double dilute" occasionally, because both dilute genes are present and have an effect on the resulting physical coat color of the dog.

Black/brindle: K, Kbr, kK>Kbr>kK plus anything = "regular" color, no tan markings; generally black unless liver, blue, isabella, merle, and/or greying is present*
KbrKbr or Kbrk = brindle tan over base color
kk = the dog will show any tan marking or possibly a varying shade of red

*The dominant K allele overrides all other color genes except for liver, blue, merle, and greying. If a dog has bb, dd, and/or Mm (even if the dog also has KK, KbrKbr, Kk, or Kbrk), the dilute, merle, and greying genes will override a black dog. Greying can also affect black coats (see the G allele below).
*The E allele will override the K allele; even if a dog is solid black (K_), but has Em_, it will display some shade of red with a mask; if it is K_ and has e_, it will display a solid shade of red. Only when the E allele is E_ will the K allele be revealed (and even then, it can be hidden under the colors listed above).
*Brindle varies in thickness/coverage, and has not been proven to be the effect of any other gene.
*There is an exception when it comes to 'red' dogs, seen above/below under the C and I alleles. If a dog has recessive red (ee), even though eumelanin pigment (the B/D/K alleles) may also be present, then the dog will look red as opposed to black/liver/blue/isabella. However, the dog's skin color will still be determined by the eumelanin pigment (the B/D/K alleles). This may be referred to as dilute factored red.
*note that the examples below are all black with tan points; the black can be replaced with liver, blue, isabella, or merle if the proper gene is present

Agouti: Ay, aw, at, aAy>aw>at>aAy plus anything = fawn (ranging from golden to cream) or sable* (ranging in intensity from lots of black to hardly any, called "clear")
awaw, awat, awa = agouti, aka "wolf agouti" or "wild"; note that "sable" GSDs are often agouti and not genetically Ay, but aw.
atat, ata = saddle/creeping tan/tan points*
aa = recessive "regular" color (often referred to as recessive black); even if the dog is kk which allows tan markings to show, if it has aa, it will appear solid and the base color will be determined by the B/D/K alleles.

*sable can be "tipped" or "shaded", as seen from the examples below
*saddle/creeping tan/tan points is only expressed if the dog also has kk and either Em or E in the genes; otherwise, it will either be black, brindle, or recessive red, and the saddle/tan genes will carry to offspring but will not show in the dog's phenotype. See here for official information.
If you use genetics in DARPG to determine between saddle or tan points, you'd first have to determine if both of those markings are possible in the breed, and if so, RNG to see whether one of those genes also contains the RALY (saddle) gene or not; YES=saddle, NO=tan points. If only one of the markings shows up in the breed, then atat and ata will only show that one marking (ie. Dobermans only have tan points and Beagles only have saddles).
*creeping tan refers to a pattern that looks like a mix of tan points and saddle; the tan reaches farther on the dog's body (covers most of the face, legs, and reaches to the chest) than traditional tan points, but does not recede far enough to be distinguished as saddle. Progression of creeping tan with age can be found here.
*note that the examples below are all black with tan points; the black can be replaced with liver, blue, isabella, or merle if the proper gene is present

Merle: M, mM>mMM = double merle
Mm = merle
mm = no merle
**Ma = atypical merle
**Mc = cryptic merle

*merle is merely a "pattern overlay" on eumelanin pigment. This means that merle only shows on genetically black, blue, liver, or isabella dogs. It would be "hidden" on a red dog (sometimes you can tell that if a red dog has blue eyes, it likely has hidden, or "phantom", merle).
*a blue merle would genetically be dd Mm and a red merle would actually be a liver merle, bb Mm.
*breeding merle is often very dangerous, as double merle dogs are almost always born with problems, or can even be stillborn! It's a highly discouraged practice; you should always breed a merle dog to a non-merle dog!
**only proven in Catahoula Leopard Dogs and Dachshunds thus far, Ma and Mc are extensions of the merle gene that also affect whether or not a dog physically displays merle, or how it is displayed. More information can be found here.

Harlequin: H, hHH = lethal
Hh = harlequin
hh = no harlequin

*harlequin is a unique gene that does not display on its own. It requires the presence of merle (Mm or MM) to show. If a dog has the Harlequin gene, but is mm, meaning it doesn't have merle, it only carries harlequin until bred to a merle.
*harlequin acts the same way that merle does in the fact that it only affects eumelanin pigmented dogs.
See the Guide to Canine Genetics II for examples of how Merle and Harlequin interact.

White (spotting): S, si, sp, sw
S>si>sp>swS plus anything = the dog will be solid; occasionally a genetically solid dog may have "residual/minimal" white (such as a small star on the chest or white toes), which is not genetic!
sisi, sisp, sisw = irish white; can be collared or not
spsp, spsw = piebald white
swsw = extreme piebald white

*the si and sw genes are technically still theoretical, but are common in DARPG to explain the varying amount of white on a dog!
*extreme piebald may also be referred to as "hooded" in certain breeds when the white covers everywhere except the head and occasionally a patch on the rump.
*some believe that irregular white markings on a dog's face is a result of irish and piebald (sisp/sisw) or a combination of (hidden) merle, but this has not been proven.

Ticking/roaning: T, tr, t
T>tr>t
T plus anything = ticking (heavier density)
Tt = ticking (lighter density)
trtr or trt = roaning
tt = clear white (no ticking)

*roaning is technically still theoretical, but commonly used to refer to the spotting of breeds like the Australian Cattle Dog or German Shorthair Pointer!
*ticking can sometimes be referred to as "belton", especially in sporting dogs!

Additional Genetic Notes (theoretical alleles)
All of the above alleles have been proven to exist in some form or fashion, but there are a few additional genes that are not technically confirmed but are suspected to have an effect on a dog's coat color or patterns.

Intensity: I, iII = red coat color will appear somewhat "bleached" from its namesake (ie. red may be closer to orange or cream); predicted to be responsible for creating "white" dogs who don't show other colors with white patterns, like Samoyeds
Ii = intensity has minimal effect on the dog's red coat color (ie. a deep mahogany red will appear more crimson)
ii = intensity has no effect on the dog's red coat color (a red dog will appear its original rich red)

*this gene is theorized to take place of the C allele above to control red intensity, according to the study from the University of Saskatchewan; in that study, the C allele instead theorizes a gene that causes albinism in some breeds.
*the intensity gene is only suspected to have an effect on pheomelanin (aka dogs who present some shade of red in their coat); does not affect eumelanin coats.
*intensity may develop over time, lightening the coat of a dog who was born with a darker shade.

Greying: G, gGG = light grey develops over time
Gg = medium grey coat develops over time
gg = dark grey coat develops over time, or no greying at all

*any dog may possess the greying gene but some breeds show it better than others; what it does is lighten the black pigment of the dog as the dog ages. In some cases, greying may only affect the muzzle area and give the dog a greyed mask even if it had no mask before.

Tweed: Tw, twTwTw: tweed
Twtw: "regular" color, carries tweed to pups if bred to another TwTw or Twtw dog
twtw: no tweed

*tweed refers to the appearance of multiple colors of merle patches, as opposed to a few "dilute" patches that may be seen in normal merles.

Urajiro: U, uUU = urajiro
Uu = "regular" color, carries urajiro to pups if bred to another Uu or uu dog
uu = no urajiro

*urajiro refers to the lightening of pigment in some breeds of dogs in the general area that tan points and/or irish white and/or agouti would change the pigment, but is suspected to be a gene unto itself.