The Hurrian language was written during a 700-year period. The earliest known document is a royal inscription dated shortly before 2000 BC (though Hurrian words and names appear in earlier documents), and the last known texts date from the late fourteenth century BC. The language was widely spoken in what is now northern Syria, northern Iraq, and southeast Turkey, and by the end of the sixteenth century BC, the kings of Mittani had united most Hurrian cities under their control. The Mitanni introduced some linguistic terms of Indo-Aryan origin, dealing for example with horse training, and gods from the Vedic (Indian) pantheon, but the language remained Hurrian.
During the fifteenth century BC there was a struggle with Egypt over control of Syria, but shortly after 1400 BC, Hurrians and Egyptians made a peace treaty, and there were dynastic marriages. A famous letter from King Tushratta of Mitanni, discovered at Amarna in Egypt, concerned his daughter’s marriage to the Pharaoh Amenhotep III, and was written in Hurrian rather than Akkadian, the usual language of diplomatic correspondence; this ‘Mitanni letter’ of about 700 lines is a primary source for learning Hurrian. Not long after these events, Hurrian power declined rapidly. The eastern territory was gradually taken over by Assyria, which moved Hurrians out and settled Assyrians in their place, but in the west, Hurrian cultic traditions and learning were preserved by the Hittites who introduced them into their capital at Hattusa in Anatolia. This is where most Hurrian texts have been found, far removed from their origin. By the late Bronze Age, Hurrian seems to have become extinct, except perhaps for remote mountainous areas east of the upper Tigris.
The only language close to Hurrian is Urartian, once spoken in what is now the extreme east of Turkey. The name Urartian is from ancient Assyrian, and is related to the Biblical name Ararat, as in the mountains of Ararat (Genesis 8:4). Texts in Urartian date to a 200-year period from the ninth century until shortly before 600 BC. This is hundreds of years after the last Hurrian documents disappear, but Urartian is closer to Old Hurrian, rather than the later version of the language, so it is not a descendent of Hurrian. The two languages simply have a common source. Some scholars believe Hurrian and Urartian to be related to the Northeast Caucasian languages, which include Chechen, but this is a distant relationship at best.
Hurrian grammar and vocabulary are imperfectly understood, though it was clearly an agglutinative language, meaning that words are built up from a sequence of units each expressing a well-defined grammatical meaning. For example case markers (more than one) may be attached to a noun, and various grammatical markers are attached to a verb. The verb comes at the end of the clause, and there seems to have been a rich inventory of different moods for the verb, not all well understood. The language is also strongly ergative.
Hurrian was written mostly in cuneiform syllables, though a few late texts found at Ugarit (modern Ras Shamra) in Syria are written in the local alphabetic script, presumably by Ugaritic scribes.
Further information on the Hurrians is given on the Wikipedia website.