There are only three kinds of human iris color, brown, blue and green. Other iris colors are variants of these three colors.
Asians are generally the darker color, which looks like black. About 80% of Nordic have blue eyes, such as the people of Iceland, the Finns and Latvia, etc. Gray eye is considered blue iris variants. Green iris is the most rare color. The European Celtic, Germanic and Slavic people take a great proportion of them. Amber is commonly seen in other animal.
It is complicated to explain very clear. Eye color is a polygenic characteristics, impacted by more than on gene. Normally speaking, babies' eye colors are similar to the eye colors of the parents for hereditary reason. This is exactly why people of the same race have similar eye color. Genes determined the what pigmentation and quantity of pigmentation of the iris and so determined the primary colors of iris. There are only three primary colors, brown, green and blue. Other colors of iris are coming from variant forms of the three color primaries. Brown is the most common color of iris, which looks like black in most cases. Iris colors include brown, light brown, amber, green and blue. Some albinos have pink iris which is very rare cases. You know there are billions of person all over the world, it is hard to predict how many eye colors there are in total. Colors introduced above are the common ones. Rare colors include red, violet and black according to some resources, but so far I didn't see these rare colors. Plus with different light, it might give a minor change to the color of iris.
It's a very interesting yet baffling question. As far as I know, eye colors are dependent upon the amount of pigment (melanin) found in the iris and how it is distributed. Basically speaking, there are brown, blue, green, grey, hazel, black and violet. Each eye color has its own subordinate colors. Take blue for example. There are aquamarine blue, Arctic blue, baby blue, cornflower blue, crystal blue, denim blue, electric blue, forget-me-not blue, gunmetal blue, indigo, laser-beam blue, sapphire, sky blue and steel blue. Other eye colors also have variations of colors. It is really hard to predict exactly how many eye colors there are in human, but I will just go with what I know. Hope to be of help.
Iris heterochromia is a kind of abnormal body which refers to that two eye iris present different color character on eye color. Especially the iris is the color of the organization by iris pigment precipitation and distribution decisions which form process in any of the above factors. It influences the pigment distribution that can cause different eye color. Human iris gezer contain only three basic kinds: brown, blue and green. Other colors iris is the three kinds of color variation. It is very difficult to define hazel. They are described as light brown or tan. Some people think that hazel is brown and blue iris in the middle of the color. The formation of the red pigment is mostly caused by the lack of the material, such as congenital albino disease. The red color is the color of red blood cells. Green is the color of the iris which is the most rare in Europe's celtics teuton and Slavic people higher proportion. The amber proportion is in Europe or hybrids. Usually the Asian people will have black eyes. Actually their black color is not that black.