Kolokoltsov (statistics, U. of Warwick) presents a textbook explaining the essentials of Markov processes and recent achievements in their construction and analysis, stressing the interplay between probabilistic and analytical tools. The first part is based on his one-semester course on Brownian motion for final year students of mathematics and statistics. Topics there include tools from probability and analysis, Markov processes and martingales, and differential equations and martingale problems. The second part draws from his own research for five chapters that are fairly independent. Among those topics are processes in Euclidean spaces, heat kernels for stable-like processes, and complex Markov chains and Feynman integral. Annotation ©2011 Book News, Inc., Portland, OR (booknews.com)