In Tatarstan (a republic of Russia where Tatar is most commonly used) and all other parts of Russia a Cyrillic alphabet is used to write Tatar; also in Kazakhstan.
Modern Latin
A Latin alphabet-based system has been used mostly in Tatarstan since 2000 and generally on the Internet, although this has been less common more recently due to the Russian law that all languages of Russia must be written in the Cyrillic alphabet.
History
Tatar's ancestors are the extinct Bolgar and Kipchak languages.
The literary Tatar language is based on Kazan Tatar's Middle (Tatarstan) dialect and the Old Tatar language (İske Tatar Tele). Both are members of the Kypchak (or Northwestern) group of Turkic languages, although they are also partly derived from the ancient Volga Bolgar language.