The first known language in Mesopotamia's civilization was Sumerian i.e. Sumeri language.
Akkadi people came and settled in Mesopotamia around 2000 BC and gradually became the major language of Mesopotamia civilization. It took the place of Sumeri language.
Akkadi language continued to flourish and it had a major language in 336 to 323 BCE during the time of Alexander.
Aramic language also became prevalent in Mesopotamia in about 1400 BC. This language was a language similar to the Hebrew language. The scope of Aramic language increased till 1000 BC and this language started to be spoken in a wide area. Even today this language is spoken in some areas of Iraq. Iraq is the place where Mesopotamia's civilization flourished.