The Basic Framework. The Structure of Groups. Lie Groups. Representation of Groups--Principal Ideas. Representation of Groups--Developments. Group Theory in Quantum Mechanical Calculations. Crystallographic Space Groups. The Role of Lie Algebras. The Relationships Between Lie Groups and Lie Algebras Explored. The Three-Dimensional Rotation Groups. The Structure of Semi-Simple Lie Algebras. Representations of Semi-Simple Lie Algebras. Symmetry Schemes for the Elementary Particles. Appendices. References. Subject Index.