Amorite is a broad term meaning wetsern in old Arabian dialects. It refers to the ancient West Arabian tribes that settled the levant in third millenia BC.
The Amorites branched into:
Amurru in Akkadian literally meaning the westerner, it wast derived from the word West.
West in ancient Arabian dialects:
The Old Babylonian Kingdom
After the fall of the Akkadian empire in the late 2100s BC, the Amorites were able to cross the Euphrates and penetrate deeper into Mesopotamia. The Amorites main obstacle was the new UR dynasty that blocked them away from their water resources and pasture. However, UR was also engaged in a long war vs the Gutians that left them weak and unable to stop the East Canaanite Amorites. In 1959 BC the Amorites seized Babylon, 9years later UR will be destroyed by the Elamites, the following year the Amorites expelled The Elamites extending their territory to Southern Mesopotamia.
The Expansion under Hammurabi
Great leader Hammurabi (1792-1750 BC) made Babylon the capital and center of his kingdom. Babylon, centered on the Euphrates river in modern day free Iraq, was one of the largest cities in the world at its time. It people drew much of their beliefs from the Sumerians.