The manual discusses the main classical and modern (Lee transformation method, CAM theory) asymptotic methods of celestial mechanics. The explicit expressions of the general and several first members of the respective series. are given. Approximation of approximation . For the first time, accurate estimates of the convergence radius of the series of the small parameter method. are given. These methods are characterized both from a theoretical and from a practical point of view.. The book is designed for students of mathematical-mechanical, physical faculties of universities and universities . It can also be useful for graduate students and specialists ..