Groups and Symmetry

The textbook "Groups and Symmetry" offers a comprehensive and accessible introduction to group theory from both theoretical and geometric perspectives. It is aimed at advanced mathematics students and does not require prior knowledge of the topics covered. The book is the second in a two-volume series and addresses a variety of central themes, including linear transformations, group actions, Sylow's theorem, simple groups, product groups, normal series, free groups, as well as symmetry groups of Platonic solids, frieze symmetries, and wallpaper symmetries. Each section concludes with a set of worked problems and supplementary exercises that challenge and deepen the readers' knowledge and skills.