The textbook (10th ed., Isp.) Sets out the main material included in the combined course of analytical geometry and linear algebra: vector algebra, lines and planes, second-order lines and surfaces, affine transformations, systems of linear equations, linear spaces, Euclidean and unitary spaces, affine spaces, tensor algebra. This edition has been substantially revised. Basically, the changes are aimed at improving the presentation, but many additions have been made, of which the most significant is Jordan's theorem. Added tasks and exercises with answers and instructions. A number of abbreviations were also made. For students of universities and technical universities with an extended mathematics program.