Exodus is named after the Greek phrase for the road out, which is an appropriate term for the events of the book. Ex 12:40 states that the time in Egypt was 430 years, but the precise dating of the events lends to two possibilities. The events can be dated in 1 Kings 6:1 to 480 years before the fourth year of the reign of Solomon, which suggests the 15th century BC. Ex 1:11 suggests that the Exodus occurred during the reign of Rameses II in the 13th century.
In Gen 17:7-8, God makes a covenant to be Abraham's god, and it is through Moses in Exodus that there is a mediator to this old covenant. Ex 19:6 describes the people of God to be a kingdom of priests and to mediate God's grace to the world, a fact that 1 Peter reminds us of.
The family of Jacob remained in Egypt, but a new regime comes to power and agitates against the Hebrews, saying that there are too many of them. The Hebrews were put to hard labor, and midwives were told to kill the male children, but the midwives feared God and did not kill them. Pharaoh demanded that the boys be cast in the Nile. Possibly for this reason, pharaoh's name is not mentioned in Exodus but the midwives, Shiphrah and Puah, are.
Moses is born to a Hebrew woman, who hides him and places him in a basket in the reeds beside the river. Pharaoh's daughter draws Moses out and names him for the word for drawing out, a Hebrew word, but one that sounds like an Egyptian name.
When Moses sees an Egyptian abusing a Hebrew, he kills the Egyptian, but this is discovered, and Moses flees, and helps a Midianite family. For this kindness, the father gives Moses his daughter Zipporah.