Henry McKean is a professor in the Courant Institute of Mathematical Sciences at New York University. He is a fellow of the American Mathematical Society and in 2007 he received the Leroy P. Steele Prize for his life's work.

• Preface; 1. Preliminaries; 2. Bernoulli trials; 3. The standard random walk; 4. The standard random walk in higher dimensions; 5. LLN, CLT, iterated log, and arcsine in general; 6. Brownian motion; 7. Markov chains; 8. The ergodic theorem; 9. Communication over a noisy channel; 10. Equilibrium statistical mechanics; 11. Statistical mechanics out of equilibrium; 12. Random matrices; Bibliography; Index.

'… packs a great deal of material into a moderate-sized book, starting with a synopsis of measure theory and ending with a taste of current research into random matrices and number theory. The book ranges more widely than the title might suggest … There are numerous exercises sprinkled throughout the book. Most of these are exhortations to fill in details left out of the main discussion or illustrative examples. The exercises are a natural part of the book, unlike the exercises in so many books that were apparently grafted on after-the-fact at a publisher's insistence. McKean has worked in probability and related areas since obtaining his PhD under William Feller in 1955. His book contains invaluable insights from a long career.' John D. Cook, MAA Reviews