Currently, the circle of people interested in celestial mechanics has expanded significantly. Meanwhile, literature in Russian on this section of astronomy is still extremely small. The existing fundamental manuals of M. F. Subbotin "The Course of Celestial Mechanics" and G. N. Duboshin "Celestial Mechanics" cover a very wide range of issues, the content of which goes far beyond university programs. In this book, the author sets himself significantly different goals. The content of the book is limited to the consideration of six methods of celestial mechanics, on which modern theories of the motion of planets, comets and satellites are actually based.