The monograph presents the results of qualitative, analytical and numerical studies of a flat circular limited task of three bodies. For the Hamilton system, the structure of the phase space in the vicinity of the fixed point and the periodic solution is studied. The results of these studies are used in the study of solutions of a limited problem at low values of the mass ratio. In the unperturbed problem, critical and generating solutions are allocated, allowing to systematize the results of calculations on the computer. The book uses methods of normal form and characteristics. For specialists in mathematics, mechanics and celestial mechanics.