A king in Babylon named Hammurabi was assisted by governors and other local administrators was the ruler.
A remarkable collection of laws known as the code of Hammurabi (an eye for an eye, a tooth for a tooth) regulated the punishment that was inflected upon citizens who misbehaved. Example if a nobleman pulls out another nobleman’s eyes his eyes should be put out too. Another example would be if a slave put out a nobleman’s eye the slave shall be put to death. How you can see they made big differences between the rich and the poor. Babylonian society consisted of three classes; the upper strata, the low strata, and the slaves. Like the Sumerians had rulers, nobles, priests, commoners, farmers and
slaves.
The Babylonians were later than the Sumerians the Sumerians got conquered by the Akkadians and then the Akkadians evolved into the Babylonians. Sumerians used cuneiform as a written language. The Akkadians spoke a Semitic language (like Hebrew or Aramaic but different from Sumerian); cuneiform script and Akkadian language blended together and that’s what Babylonians used. The Babylonians apparently preserved and adapted Sumerian myths.
Sources:
http://www.ushistory.org/civ/4b.asp
http://www.sjsu.edu/faculty/watkins/semer.htm