The book is devoted to the results and methods of research of integrable systems of classical mechanics. These include Hamiltonian systems with a finite number of degrees of freedom, which have a sufficiently large number of conserved quantities (motion integrals), so in principle the integration of equations of motion can be reduced to quadratures - the calculation of integrals from known functions. All known systems of this type are associated with Lie algebras, and their integrability is due to the presence of higher symmetries.