The following problems are considered in the book: the problem of the motion of the bodies of the solar system, the problem of the free fall of the body, the problem of the proper rotation of the moon. In the study, asymptotic methods of the theory of ordinary differential equations are used. In addition, problems of potential theory and central configurations of 4 bodies are considered (in the case when one mass is small compared to the rest). The book is intended for specialists in celestial mechanics and applied mathematicians using asymptotic methods for studying ordinary differential equations with a small parameter.