This volume contains a set of lectures and seminar talks on some recent developments in field theory (with particular emphasis on topological aspects and chiral anomalies in gauge theories) given by the authors at Tübingen University and elsewhere. The presentation of the material is not intended to be a self-contained introduction to the subject, but a workbook for the student who has a basic knowledge of quantunfield theory and who now wants to acquire some routine in doing practical calculations in a modern and still rapidly growing branch of particle physics. Therefore, the standard discussions and explanations contained in every modern textbook are omitted to a large extent, whereas the computational details are presented in much greater detail than in the usual monographs or original publications. Hence, to set the stage for the calculations presented here, the reader should first consult at least some of the papers or books cited at the end of each chapter.