Who was the author? Like Genesis and Exodus, Leviticus was recorded by Moses with Divine inspiration that makes the record inerrant in its original form.
What is the book? Though its name relates primarily to the Levites, the book itself primarily describes the ways all of the people of Israel were to be ceremonially, physically, and morally holy-first forgiven through God's service at the Tabernacle (chapters 1-16) and then manifested in the way they lived their lives (chapters 17-26).
Where was it written? Also like Genesis and Exodus, we are not told precisely where the book of Leviticus was written, but we expect Moses wrote it in the Sinai peninsula's desert.
When was it written? We can probably assume safely that Moses wrote the contents of the book down at God's direction shortly after God gave the details during the year the people were camped at Sinai, but we are not sure exactly when in the 40-year period of the wanderings in the desert he actually did record them.
Why? As God is holy, He calls for His people to be holy (Leviticus 11:44, 45; 19:2; 20:26; 21:8).
How? God's law shows us our sin, and His Gospel tells us what He has done about it. In the case of Leviticus, we realize we do not live the physically and morally holy life we should live, but we can find forgiveness through the sacrifices and other ceremonies God has instituted. While we do not follow the Old Testament system any more, all of that system points to Christ, from Whom we do in faith receive forgiveness in Word and Sacrament, just as the Old Testament people of Israel. Since the sin is spiritual and material, the forgiveness and "decontamination" is also.
For further reading on the book of Leviticus:
- Keil, C.F. and F. Delitzsch. Biblical Commentary on the Old Testament, Volume II, The Pentateuch, translated by James Martin and published in one volume with the other two on the Pentateuch. Grand Rapids, Michigan: William B. Eerdmans Publishing Company, reprinted May 1986. (The section dealing with Leviticus, "The Third Book of Moses", runs 285 pages. After my study Bible, this is what I turn to next, but it is a somewhat harder to use more-scholarly commentary.)
- Kleinig, John W. Leviticus, Concordia Commentary: A Theological Exposition of Sacred Scripture, gen. ed. Dean O. Wenthe. St. Louis: Concordia Publishing House, 2003. (A very recent and scholarly commentary. I have used it in connection with the Daily Lectionary readings and found it to be helpful. The format is such that one does not have to be a pastor to make use of the book.)