And I'm also interested in archaeological history too so books covering that would be nice as well. And not just the Middle East Bronze Age, but the world over.
I'm a Belgian history student and the book our professor used for her lectures was 'A history of the ancient Near East, ca. 3000-323 bc. (Third Edition) By Marc Van De Mieroop. It probably isn't the most famous book on the subject, but it gives you a good overview of ancient Mesopotamia from 3000 bc until the arrival of Alexander the Great.