The word Leviticus means And He Called and the author of the Book is Moses. The Book of Leviticus does not state when it was written but the date of authorship is likely between 1450 and 1400 B.C., which is the approximate time that Moses led the Israelites out of Egypt and the approximate time of Moses death.
Leviticus 1:1 And יהוה called to Moses and spoke to him out of the tabernacle of the congregation saying. C-MATS
Question: How did יהוה call to Moses? He first summoned him lovingly, saying, “Moses, Moses.” In reply, Moses would say, “יהוה, I am at Your service.” As the verse implies, the call came exclusively to Moses. יהוה‘s voice is powerful enough to shatter trees and be heard throughout the world, but it was the Divine will that it be heard only by Moses. יהוה also spoke to Balaam, but not lovingly like He spoke to Moses. Chumash
Question: Why did יהוה only speak to Moses? Normally, a burden which is heavy for one is light for two, or one heavy for two is light for four; but can a burden too heavy for 600,000 be bearable for one? Now all Israel were standing before Mount Sinai, and saying: “if we hear אֶת־ the voice of יהוה our Elohim any more, then we will die” (Deuteronomy 5:25), while Moses heard the voice by himself and remained alive. Chumash