The Sumerians were very inventive people. It is believed that they invented the sailboat, the chariot, the wheel, and the plow. For certain they developed cuneiform, the first written language, games and toys including the game of checkers, cylinder seals (used to sign legal documents like contracts), the first super hero (Gilgamesh), and many tools and implements to help with building and farming. They invented and used a system of math based on the number 60. Today we still divide an hour into 60 minutes, and put 360 degrees into a circle. Amazingly enough, we still use some Sumerian words today, words like crocus, which is a flower, and saffron which is both a color and a spice.
One of the greatest Babylonian achievements was a written set of laws.
One of the greatest Assyrian achievements was the library at Ninevah.