The last decade has seen striking progress in the subject of rermalization in quantum field theory. The old subject of perturbative rermalization has been revived by the use of powerful methods such as multiscale decompositions; precise estimates have been added to the initial theorems on finiteness of rermalized perturbation theory, with new results on its large order asymptotics. Furthermore, constructive field theory has reached one of its major goals, the mathematically rigorous construction of some rermalizable quantum field theories. For these models one can in particular investigate rigorously the phemen of asymptotic freedom, which plays a key role in our current understanding of the interaction among elementary particles. However, until this book, there has been pedagogical synthesis of these new developments. Vincent Rivasseau, who has been actively involved in them, w describes them for a wider audience. There are, in fact, common concepts at the heart of the progress on perturbative and constructive techniques. Exploiting these similarities, the author uses perturbative rermalization, which is the more widely kwn and conceptually simpler of the two cases, to explain the less familiar but more mathematically meaningful constructive rermalization.Originally published in 1991.The Princeton Legacy Library uses the latest print-on-demand techlogy to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.