The present book, stemmin g from the first four chap ters of the authors' Tensor Calculus (Moscow, 1969), constitutes a lucid and completely elementary introduction to linear algebra. The treatment is virtually self-contained. In fact, the mathematical background assumed on the part of the reader hardly exceeds a smattering of calculus and a casual acquaintance with determinants. A special merit of the book, reflecting its lineage, is its free use of tensor notation, in particular the Einstein summation convention. Each of the 25 sections is equipped with a problem set, leading to a total of over 250 problems. Hints and answers to most of these problems can be found at the end of the book.