Moses was the author of Exodus. The text intimates this in several locations (17:14; 24:4; 34:27) and tradition almost invariably affirms the same. Furthermore, a few New Testament passages allude to Moses as the author of the Pentateuch. It is possible that the book has been edited but there is no conclusive evidence.
The dating of the book depends largely on the chronology adopted by the researcher. With Moses as the author, the book of Exodus must have been written during the wilderness wanderings which occurred directly after the Exodus. Different chronologies place the date of the Exodus anywhere from 1440's to 1200's. I adopt the earlier date, which suggests that Moses finished the book sometime around 1400 B.C..
Audience and Purpose
The audience is early Israel. Moses wrote the book so that Israel would not forget the God who not only brought them up from Egypt into their own land but who also entered into a relational covenant with them. Several passages emphasize the importance of parents teaching their children what God did for them; Exodus lays out in detail exactly what that is for their posterity.
Much of Exodus reads like an enthralling narrative. Throughout the narrative apodictic and casuistic law is interspersed. These instruction sections highlight both what God required of Israel at the time and what he expected of Israel in the future. The narrative contextualizes the instruction while the instruction clarifies the point of the narrative.
The main idea is that God will make himself known by rescuing his people from servitude to Egypt in order that he may dwell in their midst and they may serve Him. A large part of the book is concerned with the identity of God. The question, "Who is the Lord?", comes up several times and it is answered finally in chapter 34. On the heels of this is the question, "Who will Israel serve, the Lord or Pharaoh?" The concept of service or worship plays a major role throughout the plague narrative and it is underscored even more in the apodictic sections which lay out exactly how Israel may serve the Lord. Lastly, that God will dwell in the midst of his people is a major concern of chapters 19-40. God rescued Israel from Egypt so that he might dwell in their midst and they would be free to worship him as their God. The law sections specify the terms of this covenantal relationship, which God is enacting by residing with his people.