Basic introductions

• The Ancient Near East: A Very Short Introduction by Amanda Podany

• Babylonia: A Very Short Introduction by Trevor Bryce

• Ancient Assyria: A Very Short Introduction by Karen Radner

More detailed overviews

• A History of the Ancient Near East, ca. 3000-323 BC by Marc Van de Mieroop

• The Ancient Near East: History, Society and Economy by Mario Liverani

• Ancient Near East: Historical Sources in Translation edited by Mark Chavalas

Civilizations of Ancient Iraq by Benjamin Foster and Karen Foster and A Short History of Babylon by Karen Radner are very good as well.

Finally, the Cultural Atlas of Mesopotamia and the Ancient Near East by Michael Roaf is a great free resource, although it's now fairly dated.