Reddit mentions of Mesopotamia: The Invention of the City

Sure. In no specific order:

Book 1

Book 2

Book 3

Book 4


None of these are specifically Biblical history, as I'm sure you'll quickly gather. To fully grasp the Old Testament, however, there are a few important areas that one must be strong in (in my humble opinion, that is): Ancient Near East history, and the New Testament, and a general understanding of Judaism and its individual history.

I've always been interested in it, but I've only just recently started studying (for fun!) about Mesopotamia in earnest. A few books that I've read and enjoyed, in addition to Roux's "Ancient Iraq" and of course Gilgamesh (Andrew George translation):

• Mesopotamia: The Invention of the City by Gwendolyn Lieck. This book examines ten notable cities throughout Mesopotamian history. It is not a comprehensive history book, but instead a "survey" style book which looks at the history, culture, religion, and politics of the individual cities and how they reflect on the region as a whole. The author also provides insight into the history of the excavation and scholarly debate for each city, including discussion of competing theories. Because of this, as well at its approachable style and more limited scope, it makes a good first read to students new to the subject.
  
  
• From Distant Days by Benjamin Foster. This book is (to the best of my understanding) an abridgment of Foster's other work, Before the Muses. While not as comprehensive as the larger work, it is somewhat cheaper and perhaps a little less intimidating. It includes the Creation and Flood myths, among others, as well as large sections of translations of prayers, hymns, proverbs, magic spells, and other categories. The author provides enough insight without bogging the reader down in minutiae.
  
  I hope those are helpful. I'm hoping to get more books in the near future, and will post regarding those as I read them.