In this book, on the basis of the theory of functions of a complex variable, special methods are developed for studying one class of differential equations of elliptic type, covering many important equations of mathematical physics. These methods, unlike known general methods, allow you to penetrate deeper into the nature of solutions of this kind of equations and more fully reveal their properties. With their help, it is possible to take a new approach to the study of classical problems, as well as to explore a number of new problems of important theoretical and applied importance.