Ishbi-Erra (reigned c. 2017-1985 B.C.E.), the king of Isin and an Amorite, gained control over Isin while he was an officer in Ibbi-Sin’s army (of the Third Dynasty of Ur). He then seceded Isin from Ur, and aided Elam and the Amorites by invading the Mesopotamian lands controlled by Ur. He became the successor to the Ur kings, thereby founding the First Dynasty of Isin during the Old Babylonian period.
The Old Babylonian period is determined more for linguistic reasons rather than political ones: Akkadian again replaced Sumerian as the written and spoken language, and culturally most of Mesopotamia began a major shift from the Neo-Sumerian or Ur III period to a new, Babylonian-centric society. Kings ceased to be considered divine about halfway through the Old Babylonian period. They were increasingly seen as guardians of their people, as well as arbiters of justice. Individuals became more powerful economically and rural areas increased in political power, as well. Eventually the official language of the area became Babylonian.
Several city-states enjoyed cultural and political power during this period: Isin and Larsa were concurrently important in Mesopotamia, and the First Dynasty of Babylon (c. 1894-1595 B.C.E.), founded by another Amorite, Sumu-abum, took its name from the flourishing of the city of Babylon.
The chronology of the Old Babylonian period can be understood by comparing the dates when different cities were dominant, namely:
First Dynasty of Isin (c. 2017-1794 B.C.E.)
Dynasty of Larsa (c. 2025-1740 B.C.E.)
First Dynasty of Babylon (c. 1894-1595 B.C.E.)
The most famous king of the Old Babylonian period was Hammurabi (reigned 1792-1750 B.C.E.), who instated his famous code of laws.