The civilization of Mesopotamia included distinct phases which are often seen as civilizations in their own right – the Sumerians, the Babylonians, the Assyrians, and the Neo-Babylonians.
Maps tracking the history of ancient Mesopotamia start at: Ancient Mesopotamia 3500 BCE
Society and culture:
An overview of Ancient Middle Eastern history, including Mesopotamia, start at Middle East 3500 BCE
Maps of the World at the time of Ancient Mesopotamia start at The World 3500 BCE
Maps which include references to Ancient Mesopotamia in their information:
History of the Ancient Middle East includes much on Mesopotamia
The Origins of Civilization has a special focus on Mesopotamia
Also, an article on the History of Elam deals with a powerful kingdom which, whilst not a Mesopotamian state per se, had a major part to play in Mesopotamian history.
Articles with references to Mesopotamia, showing its impact on different parts of the world, and vice versa:
The History of Ancient Greece – here
You might find the following useful: Sources and further reading on Ancient Mesopotamia
And whatever happened to the ancient Mesopotamians – or, to put it another way, how did ancient Mesopotamia turn into modern Iraq? Follow Mesopotamian/Iraqi history through maps, starting with Iraq 200 BCE.