The book differs from the available textbooks of mechanics by a greater than usual connection with modern mathematics. Particular attention is paid to the mutually enriching interaction of the ideas of mechanics and the geometry of manifolds .. In accordance with this approach, the central place in the book is occupied not by calculations, but by geometric concepts (phase spaces and flows, vector fields, Lie groups) and their applications in specific mechanical situations (theory of oscillations, solid mechanics, Hamiltonian formalism). Much attention is paid to qualitative methods of studying the movement as a whole, including asymptotic (perturbation theory, averaging methods, adiabatic invariants) For students of universities and universities with an advanced program in mathematics, as well as teachers and researchers .