The textbook outlines the basic material included in the combined course of analytical geometry and linear algebra: vector algebra, lines and planes, lines and surfaces of the second order affine transformations, matrix algebra and systems of linear equations, linear spaces, Euclidean and unitary spaces, affine spaces, tensor algebra. This edition has been substantially revised. The changes are mainly aimed at improving the presentation, but a number of additions have been made. The textbook is intended for university students.