From the editor's foreword: "Lectures in celestial mechanics" is a textbook according to which it is possible to begin the study of this part of astronomy, having no other training than elementary information from general mechanics and higher mathematics. But this textbook, which belongs to the pen of the brilliant scientist, is an essay in which the ideas of the basic methods of celestial mechanics are originally presented with sufficient mathematical rigor and utmost clarity. The first volume contains a detailed description of the general principles of applying the method of successive approximations to the integration of differential equations that determine the perturbed osculating elements of the orbits of planets. The second volume of Poincaré's textbook is divided into two parts. Part I, Decomposition of a Disturbing Function, deals with all the necessary questions pertaining to this important branch of perturbation theory. This includes the foundations of Bessel's theory of functions and the theory of Laplace coefficients and Newcomb operators. Here, the author pays much attention to the issues of the convergence of decompositions and treats these issues with complete mathematical rigor .. Part II of the second volume "The Theory of the Motion of the Moon" Poincaré divides into two sections, referring to the first movement of the Moon under the influence of the pulls of the Earth and the Sun, and to the second - the study of the effects of the pulls of the planets and the impact of the compression of the Earth. The exposition is based on the works of Hill, Delone and Brown, and although there are also questions about the convergence of the series, the whole theory is revised and presented as a single whole. The third volume of Poincaré's work contains The Theory of Tides, which is no longer part of celestial mechanics and is a statement of the solution of some problems of hydrodynamics. Currently, the Soviet edition of the translation of Poincaré's book includes only the first two volumes, which are combined into one. The translation is made very carefully and reproduces completely the work of the famous scientist with almost no changes. We allowed ourselves only to change the designations in some places (for example, designations for partial derivatives) and made several insignificant abbreviations. The Soviet reader will receive another book on celestial mechanics, a book of great scientific value and possessing many remarkable qualities. There is no doubt that the translation of A. Poincaré will be of great benefit to students, graduate students and all those interested in celestial mechanics, which in our age of space age has acquired a new meaning and has become a necessary link in a long chain of sciences dedicated to the study, development and use of methods of space exploration.