Walsh (U. of British Columbia) presents a textbook based on a two-semester course mainly for senior mathematics honor students. He assumes a knowledge of calculus and some analysis, but no measure theory. He begins with the basic axioms of probability and the all-important ideas of conditional probability and independence. Then he develops enough machinery to allow students to solve some problems and analyze card games and lotteries, and before anyone notices they have stumbled into the non-trivial questions, they are working out the gambler's ruin problem. Then comes chapter two. Among the topics are random variables, convergence, Markov chains and random walks, and Brownian motion. Annotation ©2012 Book News, Inc., Portland, OR (booknews.com)