The main theme of the book is the systematic presentation of the theory of analytic sets in the space of many complex variables. The results of this theory are widely used in modern works on the theory of complex spaces, on holomorphic maps, analytic continuation of functions, and a number of other branches of function theory. This topic is preceded by a statement of the necessary information from the general theory of analytic functions of many complex variables. Readers are not expected to have any preliminary information on the theory of functions of many complex variables.