Hammurabi reigned between 1790 and 1750 B.C. After 2000 BC, people living in and around the city of Babylon grew powerful. They started conquering lands around them. Hammurabi conquered the lands of Sumer and Akkad, and added them to a strong Mesopotamian empire whose capital was an enlarged Babylon.
What Hammurabi is most known for is the Hammurabi's code. The code was a set of 282 laws covering a wide range of subjects such as property, rent, and medical treatment. It was written around the same time as the law of Moses.
Some laws of the Hammurabi code would appear harsh today. But they were mostly fair. It is clear that Hammurabi was determined to not allow the powerful to oppress the weak. Like the law of Moses, it contained the principle of "an eye for an eye", punishing the offender with the same injury they caused to a harmed person.
Sources:
Fry, Plantagenet Somerset. The Dorling Kindersley History of the World. London: D. Kindersley, 1994. Print.