Yakov G. Sinai 
Probability Theory [PDF ebook] 
An Introductory Course

Sinai’s book leads the student through the standard materialfor Probability Theory, with stops along the way forinteresting topics such as statistical mechanics, notusually included in a book for beginners. The first part of the book covers discrete random variables, using the same approach, basedon Kolmogorov’s axioms forprobability, used later for the general case. The text is divided into sixteen lectures, each covering amajor topic. The introductory notions and classical resultsare included, of course: random variables, the central limittheorem, the law of large numbers, conditional probability, random walks, etc. Sinai’s style is accessible and clear, with interesting examples to accompany new ideas. Besides statistical mechanics, other interesting, lesscommon topics found in the book are: percolation, theconcept of stability in the central limit theorem and thestudy of probability of large deviations. Little more than a standard undergraduate course in analysisis assumed of the reader. Notions from measure theory and Lebesgue integration are introduced in the second half ofthe text. The book is suitable for second or third year students inmathematics, physics or other natural sciences. It couldalso be usedby more advanced readers who want to learn themathematics of probability theory and some of itsapplications in statistical physics.