This book, an abridgment of Volumes I and II of the highly respected "Group Theory in Physics", presents a carefully constructed introduction to group theory and its applications in physics. The book provides an introduction to and description of the most important basic ideas and the role that they play in physical problems. The clearly written text contains many pertinent examples that illustrate the topics, even for those with no background in group theory. This work presents important mathematical developments to theoretical physicists in a form that is easy to comprehend and appreciate. Finite groups, Lie groups, Lie algebras, semi-simple Lie algebras, crystallographic point groups and crystallographic space groups, electronic energy bands in solids, atomic physics, symmetry schemes for fundamental particles, and quantum mechanics are all covered in this compact new edition. It covers both group theory and the theory of Lie algebras. It includes studies of solid state physics, atomic physics, and fundamental particle physics. It contains a comprehensive index, and provides extensive examples.