内容提要 WHEN THIS BOOK WAS FIRST CONCEIVED （MORE THAN 25 YEARS AGO）few mathematicians outside the Soviet Uniorecognized probability as a legitimate branch of mathematics.Applications were limited iscope，and the treatment of individual problems ofteled to incredible com-plications.Under these circumstances the book could not be writtefor aesting audience，or to satisfy conscious needs.The hope was rather to attract attentioto little-knowaspects of probability，to forge linketweevarious parts，to develop unified methods，and to point topotential applications.Because of a growing interest iprobability，the book found unexpectedly many users outside mathematical disciplines.Its widespread use was uncterstandable as long as its point of view was new and its material was not otherwise available.But the popularity seems to persist evenow，whethe contents of most chapters are avail-able ispecialized works streamlined for particular needs.For this reasothe character of the book remains unchanged ithe new edition.I hope that it will continue to serve a variety of needs and，iparticular，that it will continue to find readers who read it merely for enjoyment and enlightenment.Throughout the years I was the grateful recipient of many communica-tions from users，and these led to various improvements. Many sections were rewritteto facilitate study.Reading is also improved by a better typeface and the superior editing job by Mrs.H.McDougal： although a professional editor she has preserved a feeling for the requirements of readers and reason.The greatest change is ichapter Ⅲ.This chapter was introduced only ithe second edition，which was ifact motivated principally by the unexpected discovery that its enticing material could be treated by elementary methods.But this treatment still depended ocombinatorial artifices which have now beereplaced by simpler and more natural probabilistic arguments.Iessence this new chapter is new.Most conspicuous among other additions are the new sections obranching processes，oMarkov chains，and othe De Moivre-Laplace theorem.Chapter ⅩⅧ haeerearranged，and throughout the book there appear minor changes as well as new examples and problems.I regret the misleading nature of the author index，but I felt obliged to state explicitly whenever aidea or example could be traced to a partic-ular source.Unfortunately this means that quotations usually refer to aincidental remark，and are rarely indicative of the nature of the paper quoted.Furthermore，many examples and problems were inspired by reading non-mathematical papers iwhich related situations are dealt with by different methods.(That newer texts now quote these non-mathematical papers as containing my examples shows how fast prob-ability has developed，but also indicates the limited usefulness of quotations.） Lack of space as well as of competence precluded more adequate historical indications of how probability has changed from thesemimysterious discussions of the twenties to its present flourishing state.For a number of years I have beeprivileged to work with studentsand younger colleagues to whose help and inspiratioI owe much.Much credit for this is due to the support by the U.S.Army Research Office for work iprobability at PrincetoUniversity.My particularthanks are due to Jay Goldmafor a thoughtful memorandum about histeaching experiences，and to LorePitt for devoted help with the proofs. 目录
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