Hammurabi, and the people of his empire, worshiped several gods. Their chief god was Marduk. The Babylonians
built temples, called
ziggurats, to worship their gods. The city of Babylon had an especially beautiful temple dedicated to
Marduk. It may have looked something like
this reconstruction.
From the "Enuma Elish" (this link takes you to a picture of some of the tablets written in Cuneiform, in the Akkadian language), the epic poem of this ancient religion, we learn how Marduk becomes the chief god. The people eventually called him "Bel" which means "lord." From the epic creation poem "Gilgamesh," we learn how man survived the Great Flood. The parallels between those stories from the ancient religions of Mesopotamia and the Biblical accounts of creation and the flood are inescapable. Of course, the deities are not even close since the people of Mesopotamia worshiped many gods. (Check out one of the sites that compares some of those similarities and differences. Scroll about half way down.)
Shamash was the Babylonian god of the sun. As patron of law and justice, it is Shamash who now takes center stage in the story of Hammurabi.