The book outlines the basic principles, tasks and methods of classical mechanics. Focus on the mathematical side of the subject. Mathematical models of the movement of mechanical systems are discussed , Various aspects of the theory of lowering the order of systems with symmetries, are presented. provides an overview of the most common and effective methods for integrating equations of motion, Qualitative Characteristics , impeding the full integrability of Hamiltonian systems, Variational methods of finding periodic and asymptotic movements are described , General theory of tensor invariants of equations of dynamics and , Finally, The most effective sections of classical mechanics are presented: perturbation theory and oscillation theory. The general results are illustrated by numerous examples from celestial mechanics and solid-state dynamics. For students, graduate students, teachers, researchers - mathematicians, mechanics, physicists, representatives of related specialties .