An anomaly is the failure of a classical symmetry to survive the process of quantization and regularization. The study of anomalies has played an important role in quantum field theory in the last 20 years, one which is described clearly and comprehensively in this book, the first textbook on the subject. The author approaches the subject through differential geometry, a method that has received much attention in recent years, and gives detailed derivations and calculations which will be invaluable to both students and researchers in theoretical and mathematical physics.