According to the book of Genesis, the races all came from Noah.
The human race started with Adam and Eve and grew evil very quickly. Pretty soon, “Every intent of the thoughts of his heart was only evil continually” (Genesis 6:5). When God looked at the earth He saw violence. The earth had become a terrible place to live, because lust for self-preservation had grown so strong that in order to eat and find a mate and protect their families, men were killing each other. So God said He was going to destroy all the people and start a new race with Noah and his sons (see Genesis 6:7-8). God did this by bringing a great flood upon the earth. After the flood there were Noah and his wife and their three sons, Shem, Ham, and Japheth, and their wives.
Ham became the father of the Egyptians and the Ethiopians, as well as the Canaanites who once lived in the land now occupied by Israel.
Japheth was the father of the Greeks, the people who lived in the islands of the sea and who settled Europe and Russia.
Shem was the father of the Semitic people–the Jews, Arabs and Persians.