Long Post Incoming;
One of the great books of this subject is Donald A. Mackenzie's
Myths of Babylonia and Assyria. This book was written published 1915, and while an original is a rare book worth a lot of money, it has been reprinted a number of times over the past century, so you should be able to find an edition somewhere fairly easily
I personally like
Gods, Demons and Symbols of Ancient Mesopotamia: An Illustrated Dictionary by Jeremy Black. It's is often used as a textbook for this and related subjects.
You'll also probably want to look up the Sumerians. Ancient Mesopotamia has a very interconnected web of religion and mythology, with each new culture building on the last. The Sumerians were the first major urban civilization of the region and it all began with them!
Sumarian Mythology by Samuel Noah Kramer is a good starting point.
You can also look up the mythology of Phoenician culture. This culture is the one that spawned the once great city of Carthage, and originated in the Levant contemporary with Ancient Israel and Judah. It carried on many of the aspects of Mesopotamian religion and culture after the Persians and Greeks started take over. The Phoenicians spread a lot of ancient Mesopotamian cultural ideas to the rest of the Mediterranean world.
An important thing to know about a lot of our knowledge of ancient Mesopotamian myths, is that we only really have their stories. Its not like the Mesopotamians had a bible of their own that laid it all out. If you really want to do thorough research it means reading the stories and understanding them as best as you can. Some stories you can probably find a lot of information about at online resources;
The Epic of Gilgamesh (probably already know this), is a pretty famous piece of epic literature, and contains many references to Mesopotamian myth.
The Epic of Atrahasis is a lesser known Akkadian epic. It probably predates Babylon, but it is through Babylon that we have our only extant copies.
The Enuma Elish is also calle the Babylonian Genesis. It is the Babylonian version of the creation story. Other versions of this story include the Eridu Genesis, and the Barton Cylinder. Both are Sumerian, but the former is mostly lost save for one tablet dated to 1600
BC.
The Sumerians Disputations are an alternate creation myth collection; look up "Debate Between Fish and Birds", "Debate between Sheep and Grain", and the "Debate Between Winter and Summer."
Don't be shocked if you find a lot of similarities to a religion you're already familiar with. Like I said, in this region religions built upon each other, and Judaism and Christianity both descend from this part of the world.