In what time period? I assume you mean ancient Mesopotamian?
The AskHistorians reading list contains reading suggestions for the Sumerians, Babylonians, Assyrians, Hittites, Elamites, and Persians.
I provided some reading suggestions for ancient Syria in Help/suggestions on what books to read pertaining to ancient Syrian history, the Phoenicians in this post, and Bronze/Iron Age Anatolia and Greece in this post.