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. Key Features * Covers both group theory and the theory of Lie algebras * Includes studies of solid state physics, atomic physics, and fundamental particle physics * Contains a comprehensive index * Provides extensive examples