The book describes the analytical and numerical methods of the theory of Hamiltonian systems and their applications to the study of movements close to the libration points of the limited problem of three bodies. The main attention is paid to the stability of equilibrium positions and periodic movements of nonlinear Hamiltonian systems in resonant cases, when purely imaginary characteristic indicators of the linearized system of equations of perturbed motion are connected by integer relations .. The problem of the stability of triangular libration points of a limited task of three bodies is studied in detail. A method for constructing and studying the stability of periodic movements close to the equilibrium positions of autonomous Hamiltonian systems has been developed. This method is used in the analysis of periodic movements close to triangular libration points. An approximate analytical theory of motion near the rectilinear near-lunar libration point. has been constructed.