Group theory is an important part of the M Sc chemistry curriculum of almost all universities. A proper understanding of chemical bonding and molecular spectroscopy remains incomplete without at least a preliminary knowledge of molecular symmetry aspects. This is obtained from the representation theory of groups which is explained in this text. Students with a basic knowledge of elementary quantum chemistry and mathematics will be able to benefit immensely from the book. Salient Features: All discussions begin with familiar examples and then proceed to explain the abstract concepts of group theory. The authors' approach removes the fear of abstract concepts while explaining the necessary mathematical statements and proofs. Gives the student sufficient working knowledge for applying group theory to any structural /spectroscopic problem. Students can construct simple cardboard models of the Platonic solids to help them to understand the intricate symmetry operations which are essential for exposition of molecular structure and chemical bonding. Drawing stereographic projections of the point groups and construction of symmetry multiplication tables of large groups and character tables of direct product groups have been explained in detail. The minimum required key concepts of Linear Algebra (such as vector spaces and matrices) are developed in a logical and understandable manner in a separate chapter. Each chapter contains review questions, short questions, MCQs and practice problems.