Moses is the human author of the book of Exodus. From ancient times the Jews have believed Moses wrote Exodus. It was written during the time Israel was in the desert. B.C. Genesis and Exodus are very closely connected. Genesis closes with Israel in Egypt.
Exodus begins at that point and continues Israel's history.
Exodus covers a period of about 360 years. It begins with the death of Joseph and continues to the building of the tabernacle at Mt. Sinai. The people of Israel multiplied rapidly in Egypt. After a time, a new Pharaoh came to the throne. He did not know about Joseph and how he had saved Egypt from famine.