This manual is written in accordance with the program of the course of theoretical mechanics operating at Moscow State University. The problems proposed in it illustrate the basic methods of theoretical mechanics and the application of these methods to solving specific problems. The latter is especially important when studying the course. Solving problems in theoretical mechanics poses serious difficulties for students, and it is very difficult to learn how to solve them yourself. In addition, when solving problems on your own, there is no certainty that the chosen solution is really the right one. When solving problems in the classroom, the teacher controls the solutions and, directing the independent work of students, draws their attention to the features of the studied methods. All those who study the subject on their own are deprived of such control and assistance. First of all, this manual will be intended for them, which to some extent can replace the teacher.