Leviticus starts with the words: “And the Lord called unto Moses, and spake unto him out of the tabernacle of the congregation.” Such introductory words appear over 35 times in Leviticus. They emphasize that Moses received these many revelations and communications personally and that he wrote them himself (compare Deuteronomy 31:9). – God spoke out of the tabernacle of congregation but also on Mount Sinaï (see chap. 25:1).
Thus Moses was able to write it all down and to communicate it to the people of Israel (compare Joshua 1:7-8).
The Lord Jesus testifies to the fact that Moses was the author of Leviticus in Matthew 8:4 (comp. Leviticus 13:49; Leviticus 14:2-32).
The book of Leviticus is the book of fellowship (or communion). In Exodus God saved His people and formed an alliance with them.
In Leviticus the principles of approaching God are shown. Therefore Jehovah speaks primarily out of the tabernacle of congregation in this book (chap. 1:1).
In the first seven chapters we will find the offerings which the people of Israel should bring to God. They are the expression of fellowship in worship based on atonement. Then follow the dedication of the priests who were the mediators of this fellowship in chaps. 8-10.
For many Bible readers the Old Testament sacrifices are difficult to understand. But God Himself presented this thought already to Adam and Eve when He clothed them with coats of skins (Genesis 3:21).
By this means He showed them that they could not possibly hide their guilty nakedness by their own efforts, but only by the fact that an animal died for them in their stead.
Similarly the Christians are called upon to bring spiritual and material1 offerings and even to present their bodies a living sacrifice.
All this is acceptable to God by the offering of Christ only (compare 1 Peter 2:5; Philippians 4:18; Romans 12:1).