Some say mathematicians and physicists are made for each other, while others prefer to believe they are of different species. Ma (physics, Institute of High Energy Physics, China) takes the middle road and finds common ground, explaining the fundamental concepts and techniques of group theory in language familiar to physicists. He reviews linear algebras, then describes the group and its subsets, including homomorphism of two groups and the proper symmetric group of a regular polyhedron, the theory of linear representations of groups, the three-dimensional rotation group, permutation groups, Lie groups and Lie algebras, unitary groups, real orthogonal groups and symplectic groups. This is suitable for classroom use in graduate physics courses, particularly those in theoretical physics, and also for students in theoretical chemistry.