This book deals with boundary value problems for analytic functions with applications to singular integral equations. New and simpler proofs of certain classical results such as the Plemelj formula, the Privalov theorem and the Poincare-Bertrand formula are given. Nearly one third of this book contains the author's original works, most of which were not published in English and, hence, were previously unknown to most readers in the world. This book consists of seven chapters together with an appendix: chapter 1 describes the basic knowledge on Cauchy-type integrals and Cauchy principal value...

This book is based on the teaching experience of the authors, and therefore some of the topics are presented in a new form. For instance, the multi-valued properties of the argument function are discussed in detail so that the beginner may readily grasp the elementary multi-valued analytic functions. The residue theorem is extended to the case where poles of analytic functions considered may occur on the boundary of a region -- which is very useful in applications but not seen in textbooks written in English.