This book is devoted mainly to the presentation of a number of main sections of differential geometry "as a whole." It does not cover all the variety of issues studied in this area. In particular, this did not include results related to the theory of infinitesimal and continuous bends, work on Riemannian geometry "in general," work on the theory of minimal surfaces, a number of areas of the theory of convex bodies (mixed volumes, packages and coatings, etc.), isoperimetric problems. The book includes a fairly systematic presentation of a number of initial concepts and results of general and homotopy topologies, the theory of metric spaces and the theory of partial differential equations.