The book is devoted to a new approach to the theory of relativity and its astronomical applications, based on the use of methods of modern differential geometry. Their application proved to be extremely fruitful in the study of the properties of space-time under special conditions, namely the problems of the singularity in cosmology, black holes, and so on. p. The authors examined the role of gravitation, Methods of Differential Geometry and General Relativity , The physical meaning of the curvature of space-time , exact solutions and Cauchy's problem in general relativity, The problem of the singularity and its applications to elucidating the nature of black holes and the various stages of the expansion of the universe