Any good outlines or books out there on the subject? It seems that there is so much material about Ancient Greece, Rome, and Egypt but not that much prominent stuff on Mesopotamia.
There are several quite excellent books on the subject.
This is an older, but still relevant and excellent overview of ancient Mesopotamian culture. It spans a very broad swath of time, all the way back to predynastic Uruk and Ubaid cultures.
This book is more recent, but also covers the same general stuff. Written with less flair, but perhaps more concise.
This is a series of essays/articles on Mesopotamian culture/writing. Less about the history of the region, more about how daily life and systems worked, and the details of life in ancient Mesopotamia. For when you want to know something more than just events.
Oxford handbooks are a really great resource for studying any ancient civilization. If you are curious about any culture, check out their handbooks. They get some of the best scholars on the subject to write their books.
There are many more out there, but these are a very excellent starting point. Pretty much any scholar of this area and time period will have read these books at some point in their academic career.
In addition to the excellent suggestions above 'the cultural atlas of ancient Mesopotamia' is good for light reading and looking at nice pictures and maps. http://www.worldcat.org/title/cultural-atlas-of-mesopotamia-and-the-ancient-near-east/oclc/21523764 Gwendolyn Leick's 'Mesopotamia' is a nice paper back introduction too, it's aimed at a more general audience so is a good less academic overview. http://www.worldcat.org/title/mesopotamia-the-invention-of-the-city/oclc/47903007&referer=brief_results