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. Furthermore, new experiments in atomic interferometry have been included; they have become possible by making use of modern microstructure technology. Finally, the possibility of cooling atomic beams using laser radiation has taken on increasing impor- tance; therefore we have treated this subject as well. This third English Edition cor- responds to a future Fifth German Edition. We again thank all those colleagues and students who have pointed out to us errors in previous editions. It is a pleasure for us to thank again Springer-Verlag, in particular Dr. H. Latsch, Dr. H. J. Kolsch and C.-D. Bachem for their always excellent cooperation.