The scope of this manual corresponds to the annual course of surface theory. At the same time, of course, it is assumed that the reader is familiar with the general course of differential geometry, in connection with which chapters I and III are repetitive. Elementary according to the method and chapter VI, although it discusses important classes of surfaces that are not studied in the general course of differential geometry. The nature of the presentation of the main content of the book was determined by the desire to use not only the general advantages of the tensor method, but also those features that are characteristic of the two-dimensional field.