Wallis (mathematics, Southern Illinois U.) takes a rigorous but kindhearted approach to this popular study, and includes references to classical approaches that help advanced undergraduate readers and those who wish to study on their own get a solid background from the ground up. Wallis is also careful to take on contemporary designs based on applications in a variety of fields from the very beginning, in which he introduces balanced designs and finite geometries. He proceeds to difference sets and difference methods, the "main existence" theorem, Latin squares andorthognality, one-factorization and applications, Steiner triple systems, Kirkman triple systems, Hadamard matrices, room squares and advanced applications. This is a remarkably accessible treatment of a complex topic of study. Annotation ©2007 Book News, Inc., Portland, OR (booknews.com)