Costello (mathematics, Northwestern U.) develops an axiomatic formulation of pertubative quantum field theory based on the Lagranian formalism and low-energy effective field theory. Appropriate for graduate students proficient in functional analysis, the text defines local renormalization group flow, introduces gauge theories into quantum field theory by synthesizing the Wilsonian effective action picture with the Batalin-Vilkovisky formalism, and proves renormalizability of pure Yang-Mills theory. No index is provided. Annotation ©2011 Book News, Inc., Portland, OR (booknews.com)