This text examines the statistical and quantitative techniques for performing calculations in quantum field theory. This first chapter — a survey of renormalization, functional differentiation and integration, and the Schwinger-Dyson equations — occupies about one third of the entire text. Most problems in quantum field theory can be formulated by using the functional methods described in this chapter.Additional topics include dimensional regularization; the gauge and infrared properties of quantum electrodynamics; and asymptotic behavior and renormalization group methods. This text is largely self-contained and suitable for advanced graduate students of mathematical physics. Helpful reference features include an appendix, bibliography, and index.