The material collected in this book originated from lectures given by authors over many years in Warsaw, Trieste, Schladming, Istanbul, Goteborg and Boulder. There is no other comparable book on group representations, neither in mathematical nor in physical literature and it is hoped that this book will prove to be useful in many areas of research. It is highly recommended as a textbook for an advanced course in mathematical physics on Lie algebras, Lie groups and their representations.

This book contains comprehensive reviews and reprints on dynamical groups, spectrum generating algebras and spectrum supersymmetries, and their applications in atomic and molecular physics, nuclear physics, particle physics, and condensed matter physics. It is an important source for researchers as well as students who are doing courses on Quantum Mechanics and Advanced Quantum Mechanics.