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Classical Yang-mills theory.- Path integral quantization of gauge theories.- Background field methods.- Instantons and ?-Vacua.- Schwinger model (QED)2.- Chiral anomaly in (QCD)2.- Fujikawa's path integral method.- Chiral anomaly in the Schwinger-Symanzik formalism.- Anomalous ward identities a la Wess-Zumino.- Topological aspects of the Wess-Zumino effective action.- Topological baryon number and the Skyrme model.- The Atiyah-Singer index theorem (for the Euclidean Dirac operator).- Chiral anomalies and differential geometry.- Effective gauge theory actions in (2n + 1) dimensions.- Chiral anomaly with gravitational background field.- Vacuum charge in 2n + 1 dimensions.