The book discusses the main analytical and qualitative methods, special functions and tasks of celestial mechanics. The whole presentation is based on a universal approach to the study of dynamical systems based on the theory of canonical equations. Detailed mathematical apparatus of special functions, widely used in the problems of celestial mechanics Numerous applications of analytical and qualitative methods of celestial mechanics to specific objects of the solar system and the movements of the satellite are considered The book is intended for students, graduate students and specialists in the field of celestial mechanics, physics and astronomy.