Much of the mathematical folklore passed down from advisor to student, or between collaborators, is not rigorous enough to be discussed in the formal literature. But now, such information can be communicated via the semiformal medium of research blogging. This book grew from a blog begun in 2007 by Tao (mathematics, University of California-Los Angeles), combining his own research and other recent developments in mathematics with lecture notes, non-technical puzzles, and expository articles. With material from the first year of the blog already published in book form, this book is the first volume of a two-volume set of blog posts from 2008, focusing on ergodic theory, topological dynamics, combinatorics, and number theory. It offers expository articles, self-contained lecture notes from Tao's courses, and discussion of topics including additive prime number theory, the law of large numbers, and the Lucas-Lehmer test for Mersenne primes. Some selected comments and feedback from blog readers have also been incorporated into the articles. The readership for the book includes graduate students and research mathematicians. Annotation ©2009 Book News, Inc., Portland, OR (booknews.com)