This book reproduces the doctoral thesis written by a remarkable mathematician, Sergei V. Kerov. His untimely death at age 54 left the mathematical community with an extensive body of work and this oneofakind monograph. In it, he gives a clear and lucid account of results and methods of asymptotic representation theory. The book is a unique source of information on the important topic of current research. Asymptotic representation theory of symmetric groups deals with problems of two types: asymptotic properties of representations of symmetric groups of large order and representations of the limiting object, i.e., the infinite symmetric group. The author contributed significantly in the development of both directions. His book presents an account of these contributions, as well as those of other researchers. Among the problems of the first type, the author discusses the properties of the distribution of the normalized cycle length in a random permutation and the limiting shape of a random (with respect to the Plancherel measure) Young diagram. He also studies stochastic properties of the deviations of random diagrams from the limiting curve. Among the problems of the second type, Kerov studies an important problem of computing irreducible characters of the infinite symmetric group. This leads to the study of a continuous analog of the notion of Young diagram, and in particular, to a continuous analogue of the hook walk algorithm, which is well known in the combinatorics of finite Young diagrams. In turn, this construction provides a completely new description of the relation between the classical moment problems of Hausdorff and Markov. The book is suitable for graduate students and research mathematicians interested in representation theory and combinatorics. Readership Graduate students and research mathematicians interested in representation theory and combinatorics. Table of Contents  Introduction
 Boundaries and dimension groups of certain graphs
 The boundary of the Young graph and MacDonald polynomials
 The Plancherel measure of the symmetric group
 Young diagrams in problems of analysis
 References
 Comments on Kerov's thesis by G. Olshanski
 Additional references
