A monograph devoted to qualitative studies of limited problems n>3 bodies by methods of computer algebra consists of four chapters. The first two chapters contain the theory of tomographic solutions in the problem of many bodies. The other two chapters are devoted to the study of stability in the sense of Lyapunov's new equilibrium solutions of the differential equations of limited problems of many bodies based on the theorems of CAM theory. A detailed computer implementation of Birkhoff's method of normalizing Hamiltonians' limited tasks of four, five, six, and seven bodies. For researchers, graduate students and students of mathematical specialties . Can be used in university special courses on qualitative theory of differential equations and Hamiltonian dynamics.