"The book is a very fine collection of five authoritative essays on five main directions in asymptotic probability, each giving a state-of-the-art overview as seen from Vilnius ... in 1991, when the original Russian edition was published in Moscow. Of course, any insider appreciates the relevance, indeed, the importance of the Vilnius view. The nine-year delay with this English translation (a superb job, done by B.Seckler) is unessential: while all five fields continued to develop and grow in these nine years, the essayists make honest attempts to explore the very essence of their fields, and mostly with success. Thus, most later developments of note would easily fit into the framework described in each of the five directions. ... People doing research in any of the areas above will find the volume extremely useful as a reference work that, in particular, makes hundreds of papers from Russian periodicals available for the first time. It will be practically indispensable for a graduate student beginning to do research in asymptotic probability." Sandor Csorgo, Acta Scientiarum Mathematicarum 2002, Vol. 68, pp. 1013-1014 "... This book should be at hand for any specialist on asymptotic methods in probability and statistics, and can also serve as a basic reference for graduate and Ph.D. students of stochastics." European Mathematical Society, March 2002 "The monograph is written at the research level and will be a useful reference for graduate students and teachers." Journal of the American Statistical Association

• I. Classical-Type Limit Theorems for Sums of Independent Random Variables.- II. The Accuracy of Gaussian Approximation in Banach Spaces.- III. Approximation of Distributions of Sums of Weakly Dependent Random Variables by the Normal Distribution.- IV. Refinements of the Central Limit Theorem for Homogeneous Markov Chains.- V. Limit Theorems on Large Deviations.- Name Index.