Old Babylonian was the language of king Hammurabi and his code, which was one of the oldest collections of laws in the world.
The Middle Babylonian (or Assyrian) period started in the 1500s BCE. The division comes from the Kassite invasion of Babylonia around 1550 BCE, and their reign for 300 years. The Kassites gave up their own language in favor of Akkadian, but they had little influence on the language. At its apogee, Middle Babylonian was the written language of diplomacy of the entire ancient Orient, including Egypt. During this period, a large number of loan words were included in the language from North West Semitic languages and Hurrian; however, the use of these words was confined to the fringes of the Akkadian speaking territory.