Tocharian B, an Indo-European language spoken and written in the first millennium C.E. in parts of what is now the Tarim Basin of western China, is of great importance to numerous disciplines, from Indo-European historical linguistics to the study of Central Asia, the Silk Road and Buddhism.This first-ever textbook in the language makes Tocharian B, hitherto familiar mostly to specialists, readily accessible to a broad audience. In twenty graduated lessons, the student is introduced to all the language's grammar, with translation exercises between English and Tocharian in both directions and numerous passages taken from original texts. The book assumes no familiarity with the scholarly disciplines above, but simultaneously contains much information useful to specialists by virtue of the author's broad knowledge and familiarity with the most up-to-date literature. A full glossary, together with tables of declensions and conjugations, key to the exercises, and bibliography round out the volume.The Tocharian B texts that Weiss uses as the basis for his grammar date from the 5th to 10th centuries, but were not discovered until the early 1900s. Many of them are Buddhist religious texts, but other documents include caravan passes from the Silk Road, economic documents from Buddhist monasteries and a famous love poem.The language is now extinct, with scholars surmising that it was eventually supplanted by the Uyghur language. It is important linguistically because, as a separate branch of the Indo-European family, it contributes unique evidence to scholars’ understanding about what the ancestor language would have been like. It is also important culturally because the Tocharians were probably one of the main vectors of the transfer of Buddhism from India to China..