The ?rst edition of this textbook had found a friendly acceptance. This second edition does not change the concept of the representation which combines the - perimental techniques for the investigation of atoms and molecules and their results that have lead to the development of quantum physics. Some new developments in laser physics and quantum optics have been inserted in Chapter 12 in order to give the reader some ideas about the frontiers in these ?elds regarding experimental techniques and physical insight. This second edition represents a thoroughly revised version of the ?rst edition, which, unfortunately, contained a lot of errors and misprints. I am grateful to many readers who have informed me about such errors and who offered corrections and improvements of the representation for a better understanding. I am particularly - debted to Dr. Nico Dam, Raboud University Nijmegen, Netherland and Prof. Zamik Rosenwaks, Ben Gurion University, Israel, who have sent me an extensive correction list. The author hopes, that this new edition will be well accepted and that critical readers will send their comments or ideas about possible improvements. I thank Dr. Th. Schneider, Springer Verlag for his continuous interest and encouragement.