This is a good, basic history of the inhabitants of Mesopotamia in the ancient times. It is a thematic rather than chronological study. It will give you a good general understanding of the institutions and structures of Mesopotamian culture and society.
Really a fine History of the area roughly known as Babylon, now Iraq, and the surroundings. Well worth the read for anyone interested. It stops with Roughly the Conquest by Alexander. Good information on the lives and life styles not just some wars.