This monograph, first published in Russian, presents a new efficient tool of computational mechanics, complex variable boundary integral equations (CV-BIE). The book is conceived as a continuation of the classical monograph by N.I. Muskhelishvili into the computer era. The English edition places more emphasis on problems relating to media with internal structure; it contains more examples showing the potential and advantages of the analysis. The book may be of use to those who want to calculate stresses, strains, stress intensity factors and effective properties of a medium with internal structure when dealing with problems of materials science, fracture mechanics, micromechanics, soil and rock mechanics, geomechanics, civil and mechanical engineering. It may also serve as a textbook for graduate students on the theory of real potentials, on the CV-BIE and on the CV-BEM.