This fourth edition contains a few additional figures. Otherwise only typographical er- rors have been removed. The final chapter on Fundamentals of the Quantum Theory of Chemical Bonding is continued in an extended way in the textbook Molecular Physics and Elements of Quantum Chemistry by the same authors. This book contains, in particular, a profound presentation of group theory as applied to atoms and molecules. Furthermore, the in- teraction between atoms and molecules and light is treated in detail. We thank again Springer-Verlag, in particular Dr. H.1. Kblsch and Mr. C.-D. Bachem for their excellent cooperation as always, and Prof. W. D. Brewer for his con- tinuous support in translating our German text. Stuttgart, February 1994 H. Haken H. C. Wolf Preface to the Third Edition The second edition of this book again enjoyed a very positive reception from both uni- versity teachers and students. In this edition we have removed all of the typographical errors that came to our attention. In order to keep the book as current as possible, new developments in the direct observation of individual atoms in electromagnetic traps (Paul traps) and of atoms in molecules on solid surfaces using the scanning tunnel microscope have been added to this edition.