'… Professor Nimrod Moiseyev, one of the pioneers in [the] field, does a beautiful job detailing the mathematical underpinnings and describing a myriad of applications ranging from atomic and molecular physics, molecular spectroscopy, chemical reaction dynamics, and electromagnetic wave propagation. Throughout … one finds numerous exercises whose solutions (also provided in good detail) offer the reader much additional insight into both the mathematical intricacies of non-Hermitian quantum theory and its connections to experimental laboratory observations. At the end of each chapter, Moiseyev provides further reading references organized to make connections to the topics covered in the respective chapter and includes references from very diverse sciences. Seldom does one find a book that can be used as a student text for a graduate-level class and that treats its topic at a cutting-edge research level. Professor Moiseyev has produced such a gem in this case!' Jack Simons, University of Utah