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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.
Then the next milestone in the timeline of Mesopotamia was Hammurabi who was the sixth king of Babylon. Hammurabi is known for the set of laws called Hammurabi's Code, one of the first written codes of law in the recorded history (1728 BC to 1685 BC.) 1600-1100 BC staggered periods of Hittite hegemony over Mesopotamia.