The Epic of Gilgamesh was originally a Sumerian work of literature and therefore predates the Babylonians. However, the Babylonians continued to read and adapt this epic and therefore we can learn quite a bit about them through studying this work.
The Epic of Gilgamesh reveals a lot about Mesopotamian religion. We see that they were polytheistic with numerous gods who take human form. We learn that the goddess Ishtar had significant importance. Numerous times, Gilgamesh interacts with these gods, indicating that ancient Mesopotamians believed that humans had a role in determining their destiny. We also see that they believed in an afterlife, as Gilgamesh journeys there to rescue Enkidu. In this episode, we also see that the Babylonians held on to the belief that the dead could be reunited in the afterworld.
This work also paints a picture of a patriarchal society in which women (at least mortal ones) have little agency and no power. Politics was a purely masculine domain. Indeed, King Gilgamesh has only men to advise and counsel him. The powerful immortal women, particularly Ishtar, were not subject to these restrictions, but it can be noted that these female gods take actions and behaviors that were similar to the way that men would act or behave—likely to showcase their power and gain the obedience of their followers.
The Epic of Gilgamesh also shows us several ways in which ancient Mesopotamian society was stratified. Gilgamesh and his advisors represent the ruling and warrior class. The Babylonians relied heavily on the agricultural output of the Fertile Crescent and built large cities. This would not have been possible without ruling and working classes—something that is referenced several times in this epic.