The present book grew out of lecture notes prepared for a "Cours du troisieme cycle de la Suisse Romande", 1983 in Lausanne. The original notes are considerably extended and brought up to date. In fact the book offers at many instances completely new derivations. Half-way between textbook and research monograph we believe it to be useful for students in elementary particle physics as well as for research workers in the realm of supersymmetry. In writing the book we looked back not only on ten years of super- symmetry but also on ten years of our own life and work. We realize how deeply we are indebted to many friends and colleagues. Some shared our efforts, some helped and encouraged us, some provided the facili- ties to work. Their list comprises at least C. Becchi, S. Bedding, P. Breitenlohner, T. E. Clark, S. Ferrara, R. Gatto, M. Jacob, W. Lang, J. H. Lowenstein, D. Maison, H. Nicolai, J. Prentki, A. Rouet, H. Ruegg, M. Schweda, R. Stora, J. Wess, W. Zimmermann, B. Zumino. During the last ten years we had the privilege to work at CERN (Geneva), Departement de Physique Theorique (University of Geneva), Institut fUr Theoretische Physik (University of Karlsruhe) and at the Max-Planck-Institut fUr Physik und Astrophysik (Munich) for which we are most grateful. Grate- fully acknowledged is also the support we received by "the Swiss National Science Foundation" (O. P. ), the "Deutsche Forschungsgemeinschaft" (Heisenberg-Fellowship; K. S. ).