Following the same successful approach as Dr. Burn’s previous book on number theory, this text consists of a carefully constructed sequence of questions that will enable the reader, through participation, to study all the group theory covered by a conventional first university course. An introduction to vector spaces, leading to the study of linear groups, and an introduction to complex numbers, leading to Mobius transformations and stereographic projection, are also included. Quaternions and their relationships to 3-dimensional isometries are covered. The book’s climax is a study of the crystallographic groups, with a complete analysis of these groups in two dimensions.