The following additions and changes have been made to the present edition:: : [ In Chapter I, the results are given , [CM concerning the Cauchy formula and Cauchy integrals using Lebesgue integrals in Chapter III, the presentation of the approximate calculation of integrals by the method of rapid descent has been changed and the presentation of the stationary phase method in Chapter IV has been added to the presentation of the theory of analytical functions of a single matrix.. [DT ) Major changes made to Chapter V. In particular, a brief theory of Airy functions has been added, the asymptotics of solving one linear second-order equation containing a large parameter has been considered, and the presentation of the theory of one second-order differential equation with a periodic coefficient. has been expanded. In Chapter VI, the asymptotic of the Hankel and Bessel functions is modified with a large badge and argument. They helped me a lot with these questions.... M. Babich, W. C. Buldyrev and V. A. Yakubovich . I give them my deepest thanks. Without their help I could not have done much work in preparing this edition of Volume 3.