A few additions, which did not change the structure and level of presentation, have been included in the preparation of this English translation. Chapter 1 is supplemented by Section 1.8. In Chapter 2 insertions have been added to Subsection 2.1.3; this chapter is supplemented by Subsection 2.2.4 and Section 2.7; Section 2.6 is supplemented by Subsections 2.6.2 and 2.6.6. In Chapter 3, Sections 3.1, 3.3 and 3.6 are supplemented, and a new section, Section 3.4, is introduced. In Chapter 5, Subsection 5.2.6, item (g) in Section 5.4 and Section 5.9 have been added. Subsection 6.1.3 has been added to Chapter 6. In the main, the option of using certain parts of the book as a textbook, as well as the independence of the chapters, is preserved.

After the Russian edition of the book had appeared, a number of significant monographs on combinatorics and closely related problems were published. These books and some papers have been included in the Bibliography.

I am grateful to Professor B. Bollobás for his kind suggestion to Cambridge University Press to publish this book in English, and to Professor V. F. Kolchin for useful discussions during the translation.