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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.
Hammurabi's code is important in that (1) it created a common legal framework for the various communities over which Hammurabi ruled and (2) it worked toward the elimination of personal vengeance, substituting the rule of law, meaning that disputes involving violence were less likely to escalate.