The tablet containing the Sumerian creation story was found at Nippur and dates back to 1600 BC, which was during the Babylonian dynasty. The tablet is commonly known as the Eridu Genesis.
The tablet is missing many chapters, apart from the creation, the building of cities, and the flood.
In the beginning there was only the primordial sea, Nammu, who created Anki, the universe. Together they created Enlil, the air who pushed Namu and Anki apart. The earth was known as Ki, and later became Enki, god of water and vegetation.
The rivers and the animals were created. One evening the gods were having a banquet with too much wine involved and the created humans out of clay. Unfortunately the lack of interest in creating this race resulted in them being weak mentally and physically, so the gods decided to destroy the human race by a great flood.
Only two people were credited with survival, Ziusudra and his wife. They created a massive ark (this story is starting to sound familiar), and Enki destroyed the earth over-flowing the Euphrates and Tigris rivers.
Finally the flood dried up, and Ziusudra and his wife created a strong and prosperous race of humans.