Many stories in Sumerian religion are homologous to stories in other middle-eastern religions. For example, the biblical account of the creation of man as well as the flood narrative are very similar to Sumerian tales. Gods and goddesses from Sumer have distinctly similar representations in the religions of the Akkadians, Caananites, and others. There are a number of related stories and deities shared with the Greeces as well; for example Innana's descent into the underworld is strikingly similar to the story of Persephone.
The universe was created when Nammu, a presumably formless abyss, curled in upon herself, and in an act of self-procreation gave birth to An, god of heaven and Ki, goddess of Earth (commonly referred to as Ninhursag).
The union of An and Ki produced Enlil, lord of wind, who eventually became leader of the pantheon. After Enlil is banished from Dilmun (the home of the gods) for raping Ninlil[?], Ninlil has a child, Sin (god of the moon), also known as Nanna. Inanna (goddess of love and war) and Utu/Shamash (god of the sun) were children of Sin and Ningal[?]. During Enlil's banishment, he fathers three underworld deities with Ninlil, the most notable being Nergal.
Nammu also gave birth to Enki, god of the watery abyss, or the Abzu. He also controlled the Me, holy decrees that governed such basic things as physics and complex things such as social order and law.
This accounts for the origin of most of the world as we know it.