Below is a very basic explanation of color genetics, mostly meant to help you understand what letters represent the genetic markers responsible for certain colors.
There are two widely accepted "base" colors. Black or red (chesnut/sorrel). Every horse is either black based or red based. This is shown with E (black) and e (red). Other colors are the result of modifiers and dilutions that play off the base color.
E - represents Black. It is dominant. e - represents red. It is recessive.
Every horse will receive two of these genes. One from each parent. It can be in one of 3 combinations.
EE - Homozygous black, the horse will be black based and only pass E (black) to its offspring. Ee - Heterozygous black, the horse will be black based, but may pass either E (black) or e (red) to its offspring. ee - Homozygous red, the horse will be red based and only pass e (red) to its offspring.
Black (Ee) Chestnut (ee)
A - represents agouti. Agouti is responsible for turning a black horse "bay." It will have no known effect on the color of a chestnut/sorrel. At - represents another form of agouti. It is responsible for turning a black horse "seal brown." It will have no known effect on the color of a chestnut/sorrel.
At is newly discovered and only recently able to be tested for. Formerly, a horse that carried At would test positive for A, but now a test can provide a more specific answer to a horses color. Horses with A tend to be a brighter or redder bay whereas At horses may be a more muddy and dark colored bay.