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This book covers inequalities, characteristic functions and convergence, the law of large numbers, the central limit theorem and the law of the iterated logarithm. This revised edition updates core material, and offers scores of new problems and exercises.

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Like its predecessor, this book starts from the premise that, rather than being a purely mathematical discipline, probability theory is an intimate companion of statistics. The book starts with the basic tools, and goes on to cover a number of subjects in detail, including chapters on inequalities, characteristic functions and convergence. This is followed by a thorough treatment of the three main subjects in probability theory: the law of large numbers, the central limit theorem, and the law of the iterated logarithm. After a discussion of generalizations and extensions, the book concludes with an extensive chapter on martingales. The new edition is comprehensively updated, including some new material as well as around a dozen new references.

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Preface to the First Edition.- Preface to the Second Edition.- Outline of Contents.- Notation and Symbols.- Introductory Measure Theory.- Random Variables.- Inequalities.- Characteristic Functions.- Convergence.- The Law of Large Numbers.- The Central Limit Theorem.- The Law of the Iterated Logarithm.- Limited Theorems.- Martingales.- Some Useful Mathematics.- References.- Index.

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From the reviews of the second edition:
"This book of over 600 pages gives a self-contained presentation of modern probability theory. This is an updated edition of an elementary introductory book on probability theory ... . Suitable as a textbook for beginning students in mathematics, statistics, computer science or economics ... . Also, it will be very useful to students and researchers in mathematics or theoretical physics." (Teodora-Liliana Radulescu, zbMATH, Vol. 1267, 2013)

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Allan Gut is Professor of Mathematical Statistics in the Department of Mathematics at Uppsala University, Sweden.

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