This collection contains more than a thousand tasks and exercises in the main sections of the course of differential geometry, read at the physics and mathematics faculties of universities. In preparing this publication, the authors sought to take into account the changes that are currently taking place in the teaching of mathematics. In their presentation, the authors sought to link the course of differential geometry with other mathematical courses. The apparatus of linear algebra, mathematical analysis and differential equations is significantly used. Particular attention is paid to the connection with the courses of high school geometry and analytical geometry.