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Hammurabi's Code of ancient Mesopotamian society was important because it listed the laws and the corresponding punishments.   Hammurabi's Code of ancient Mesopotamian soci â¦ ety was important because it listed the laws and the corresponding punishments.   the first time laws were put into writeing.
Perhaps the most important advance made by the Mesopotamians was the invention of writing by the Sumerians. With the invention of writing came the first recorded laws called Hammurabi's Code as well as the first major piece of literature called the Epic Tale of Gilgamesh.The Wheel.erhaps the most important advance made by the Mesopotamians was the invention of writing by the Sumerians. With the invention of writing came the first recorded laws called Hammurabi's Code as well as the first major piece of literature called the Epic Tale of Gilgamesh. The Wheel.