During the last two decades a vast number of articles have been published in which probabilistic methods have been used successfully to solve combinatorial problems, and especially to obtain various asymptotic results concerning some or other characteristic of combinatorial objects. This book is aimed at readers interested in problems of this kind both from the theoretical point of view and from the point of view of possible applications.

The book may be used by students and postgraduates in combinatorics and other fields where asymptotic methods of probability theory are applied. In particular, the material contained in this book could be taught in courses on combinatorial structures such as graphs, trees and mappings with an emphasis on the asymptotic properties of their characterictics. We believe that the asymptotic results presented here provide specialists in probability theory with new examples of applications of general limit theorems.

This text assumes a standard graduate-level knowledge of probability theory and an aquaintance with typical facts drawn from a general introduction to functions of complex variables. For the reader's convenience, the relevant results of probability theory are briefly reviewed in Chapter 1. The preliminaries from combinatorial analysis are given in the introductions to each of the subsequent chapters. Readers who are interested in obtaining more detailed knowledge of the corresponding aspects of combinatorics are advised to study my book ‘Combinatorial Methods in Discrete Mathematics’ or any other basic course devoted to this subject.