Patriarchal Period from c. 1800 B.C. to perhaps 1500 B.C.
This is the time from before the Hebrews went to Egypt. Technically, it is a period of pre-Jewish history, since the people involved were not yet Jewish.
A Semite from Ur in Mesopotamia (roughly, modern Iraq), Abram (later, Abraham), who was the husband of Sarai (later, Sarah), goes to Canaan and makes a covenant with God. This covenant includes the circumcision of males and the promise that Sarai would conceive. God renames Abram Abraham and Sarah Sarai. After Sarah gives birth to Isaac, Abraham is told to sacrifice his son to his God. This story is like the one of Agamemnon's sacrifice of Iphigenia to Artemis. In a Hebrew version as in some of the Greek, an animal is substituted at the last minute. In the case of Isaac, a ram. In exchange for Iphigenia, Agamemnon was to obtain favorable winds so he could sail for Troy at the start of the Trojan War. In exchange for Isaac, nothing was offered initially, but as a reward for the obedience of Abraham, he was promised prosperity and more offspring.
Abraham is patriarch of the Israelites and Arabs. His son by Sarah is Isaac. Earlier, Abraham had had a son named Ishmael by Sarai's maid, Hagar, at Sarai's connivance. The Arab line runs through Ishmael. Later, Abraham bears more sons, Zimran, Jokshan, Medan, Midian, Ishbak, and Shuah, to Keturah, whom he marries when Sarah dies. Abraham's grandson Jacob is renamed Israel. Jacob's sons are the fathers of the 12 Hebrew tribes.
IsaacThe second Hebrew patriarch was Abraham's son Isaac, father of Jacob and Esau.
JacobThe third patriarch was Jacob who, like his grandfather, received a name change to Israel. He was patriarch of the tribes of Israel through his sons. Because there was a famine in Canaan, Jacob moved the Hebrews to Egypt but then returned. Jacob's son Joseph is sold to Egypt and it is there where Moses is born c. 1300 B.C.
There is no archaeological evidence to corroborate this. This fact is important in terms of the historicity of the period. There is no reference to the Hebrews in Egypt at this time. The first Egyptian reference to them comes from the next period, but by then they're no longer in Egypt.
Some think that the Hebrews in Egypt were part of the Hyksos, who ruled in Egypt. The etymology of the names Hebrew and Moses are debated. Moses could be Semitic or Egyptian in origin.