The main sources I have used for the history of ancient Mesopotamia are:
Roux, G., Ancient Iraq, Penguin, 1992, is a very readable overview of the subject for the general reader.
Saggs, H.W.F. The Babylonians, Macmillan, 1988, is, despite its name, a comprehensive and scholarly coverage of ancient Mesopotamian civilization up to the end of the Neo-Babylonian empire in the 6th century BC.
Roaf, M., A cultural atlas of Mesopotamia and the Ancient Near East, Andromeda, 1990, is a superbly illustrated and highly informative introduction to the subject.
A lavishly illustrated work on archaeology for the general reader which includes good coverage of ancient Mesopotamia, is Renfrew, C. (ed.), Past Worlds: The Times Atlas of Archaeology, Times Books, 1995, p. 98-9; 122-7; 132-5; 154-7.
A work on general archaeology aimed more at students, but readable and with very good coverage of ancient Mesopotamia, is Scarre, C. (ed.), The Human Past, Thames & Hudson, 2005, p. 232, 432ff.
For an insightful look at government in ancient Mesopotamia, see Finer, S. E., The History of Government, I, Ancient Monarchies and Empires, OUP, 1999, p. 104ff.
The University of Chicago has produced a superb site on Ancient Mesopotamia.
An informative website on ancient Mesopotamia is the British Museum’s Ancient Mesopotamia.
Wikipedia of course has a vast amount of information on Ancient Mesopotamia.