This book is devoted mainly to the presentation of a number of main sections of differential geometry "in general" .. It does not cover the whole variety of issues studied in this area. In particular, this did not include the results related to the theory of infinitesimal and continuous bending, 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, packaging and coatings, etc.). d. ), isoperimetric problems. The book includes a fairly systematic presentation of a number of initial concepts and results of general and homotopic topologies, the theory of metric spaces and the theory of partial-derivative equations.