Assyrian is a Semiticlanguage that was spoken in the ancient kingdom of Assyria. It was originally a dialect of Akkadian.
Around the 8th century BC, during the Neo-Assyrian Empire, Aramaic became the dominant as the language of the empire. Assyrian died out in the following centuries. (The modern language Assyrian Neo-Aramaic is derived from Aramaic, not Assyrian.)