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.