Amorites had managed to gain control of most of the Mesopotamian region. Like the Akkadians, the Amorites centralized the government over the individual city-states and based their capital in the city of Babylon
The Sumerian monarchy underwent significant changes; in order to justify the enormous power the monarch enjoyed, the Old Babylonians believed that the monarch was a god and had a divine origin. This powerful new monarchy invented new ways to adminster the state and its resources: taxation and involuntary military service. Above all, the greatest innovation was centralization. While the Sumerian civilization consisted of independent and autonomous city-states, the Old Babylonian state was a behemoth of dozens of cities. In order to make this system work, power and autonomy was taken from the individual cities and invested in the monarch. As a result, an entirely new set of laws were invented by the Old Babylonians: laws which dealt with crimes against the state.
It is in the realm of law that the Sumerian state was most dramatically changed by the Amorites. While law among the Sumerians was administered jointly by individuals and the state, the Old Babylonians allowed the state to more actively pursue and punish criminals. The punishments became dramatically more draconian: the death penalty was applied to many more crimes, including "bad behavior in a bar."
Perhaps the most important legal text in history is an Old Babylonian code of laws written by Hammurabi (around 1792-1750 BC), the most famous of the Old Babylonian monarchs. This code, called the Code of Hammurabi (I wonder why?) is generally regarded as Sumerian in spirit, but with all the harshness of the Old Babylonian penalties.
Although we know nothing of Old Babylonian religion, they seem to have adopted whole-cloth the religion of the Sumerians. We do know that the Amorites lived in close contact with the Sumerians for a long time preceding their ascendency over the region, so it's possible that they gradually adopted Sumerian religion over several centuries. The Amorites did, however, import a new god into Sumerian religion, Marduk, which they elevated to the supreme position over the other gods. Like the Sumerians, the Amorites did not believe that life after death held any promise or threat, so like the Sumerians, Amorite religion ruthlessly focssed on this world.
Among the great literary achievements of the Old Babylonians was the compilation of a series of Sumerian stories surround the legendary king of Uruk, Gilgamesh. This collection tells how this king destroyed the demon of the Lebanese cedar forests, defied the gods, and discovered the secret of the flood and its survivor. The Assyrian version of the collection is part of your reading assignments.