Linguists and specialists on Siberia are generally familiar with the name Ket, which designates a small ethnic group on the Yenisei and their language, widely regarded as a linguistic enigma in many respects. Ket is a severely endangered language with today less than 500 native speakers. Together with Yugh, Kott, Arin, Assan and Pumpokol, all of which are completely extinct, it forms the Yeniseic family of languages, which has no known linguistic relatives. This Grammar of Ket constitutes the first book of its kind in English and is structured as follows: (1) Introduction; (2) The Kets and their Language; (3) Phonology; (4) Morphology; (5) References. A second volume is planned on Ket syntax, supported by a collection of original texts with translations and annotations.