This book grew out of a one-term course on renormalization at ETH Zürich. It provides a mathematically rigorous, yet simple and clear introduction to that subject. It can be read by students from the third year on and it leads the reader to a level where he or she can start reading the current research literature. The book gives a thorough introduction to field-theoretic techniques such as Feynman graph expansions and renormalization. Special effort has been made to make all proofs as simple as possible by using generating function techniques throughout. Renormalization is done by using an exact renormalization group differential equation. This technique, developed during the last few years and now appearing in a textbook for the first time, provides simple but complete proofs of renormalizability theorems.