Before the Mittanni
The Hurrian language was very different from Sumerian and Akkadian; presence of distinctive Hurrian names helps to trace when and where Hurrians were present. Also, cuneiform clay tablets from the Mittanni have been found amongst the El Amarna letters. Hurrians entered Mesopotamia from the north as early as the Agade period, possibly from a homeland in highland Armenia. Short-lived minor Hurian states existed by the Agade's end, and Hurrians existed north of the river Diyala by the Third Dynasty of Ur. By Shamshi-Adad I's reign, Hurrians had fully permeated northern Mesopotamia and Hurrian princes ruled west of the Tur Abdin. The Zagros also had a strong Hurrian element; a grandson of Shamshi-Adad I even married a princess of a powerful Hurrian tribe. Less than a century after Shamshi-Adad I, Hurrians were an important element in Alalakh. Hurrians were still a loose confederation in the 17th CENT BCE text, as evidenced by a text from this time that mentions four kings of Hurrian people. However, Hurrians had a cohesive enough identity that a Hittite king's inscription describe an attack by Hurrians (and Hanigalbat, another term for Hurrians).
Just after BCE, a Hurrian kingdom called Mittanni has arisen just east of the Euphrates and which was more powerful than its Hurrian neighbors in Syria and Cilicia. The Mittanni kingdom negotiated -- and even fought -- on equal terms with the Hittites and Egypt, the two other main powers of the 2nd MILL BCE. In BCE, a Mittanni king clashed with Tuthmosis III as Egypt seized Syria and even penetrated as far as the Euphrates. Assyria, Babylonia, Hittites and other Near Eastern states sent congratulatory presents to Tuthmosis III for defeating the Mittanni. Shortly thereafter, the Mittanni king Saustatar annexed Assyrian territory and reduced Assyria to vassaldom, as described in the timeline of Assyria.
Saggs, 1985. The Might That Was Assyria.