This book, written by wellknown experts in the field, offers a concise summary of one of the latest and most significant developments in the theoretical analysis of quantum field theory. The renormalization group is the name given to a technique for analyzing the qualitative behavior of a class of physical systems by iterating a map on the vector space of interactions for the class. In a typical nonrigorous application of this technique, one assumes, based on one's physical intuition, that only a certain finite dimensional subspace (usually of dimension three or less) is important. The material in this book concerns a technique for justifying this approximation in a broad class of fermionic models used in condensed matter and high energy physics. This volume is based on the Aisenstadt Lectures given by Joel Feldman at the Centre de Recherches Mathématiques (Montréal, Canada). It is suitable for graduate students and research mathematicians interested in mathematical physics. Included are many problems and solutions. Titles in this series are copublished with the Centre de Recherches Mathématiques. Readership Graduate students and researchers interested in mathematical physics. Reviews "The text is written very clearly, carefully, and concisely. ... an excellent technical introduction for graduate students and researchers..."  Zentralblatt MATH "The book ... is a clear exposition of the basic techniques of the renormalization group applied to fermionic models, and it contains plenty of examples and problems (with the corresponding solutions), so that it can be considered a good introduction for everyone who wants to get acquainted with the field before tackling more technical papers."  Mathematical Reviews Table of Contents  Fermionic functional integrals
 Fermionic expansions
 Appendix A. Infinitedimensional Grassman algebras
 Appendix B. Pfaffians
 Appendix C. Propagator bounds
 Appendix D. Problem solutions
 Bibliography
