The authors are honored by the publication of the English edition by Cambridge University Press, edited by two colleagues who are well known for their work in fluid mechanics – Professor A. F. Messiter of the University of Michigan and Professor M. D. Van Dyke of Stanford University. The authors are deeply indebted to them for their interest in this book, the initiative for the translation into English, and for their considerable effort in the editing, which has no doubt improved the original text. Our work rests heavily on the present state of development of the asymptotic analysis of problems in fluid mechanics, which in many respects is due to Professor Van Dyke and Professor Messiter.

Since the publication of the Russian edition of this book in 1987, there have appeared numerous papers devoted to the asymptotic theory of separated flows. Therefore, in the preparation of the English edition the authors have attempted to bring the book more up to date. In particular, Chapters 2 and 6 have been expanded by the addition of two new sections, (Section 4 and Section 6, respectively) and Chapter 7 has been completely revised. Elsewhere we have confined ourselves to improvements and short additions in the text and to expanding the list of references.