This classic text is devoted to describing crystal structures, especially periodic structures, and their symmetries. Much of its content is essential to serious students of solid state chemistry and related sciences, which include mineralogy, materials science, and solid state physics. The treatment is the product of decades of research by authors Michael O'Keeffe and Bruce G. Hyde, and it provides a solid foundation for those entering the field. The first three chapters introduce point and space symmetry groups using crystallographic conventions. With this background, students will be able to understand useful information from the crystallographic literature. Chapter 4 treats crystal geometry and features a discussion of transformations of coordinate systems. Chapters 5 through 7 are devoted to the description of simple geometric patterns that underlie crystal structures.  Exercises and notes follow each chapter, and the text concludes with several appendixes. Updated material prepared for this Dover edition by Professor O'Keeffe and Dr. Proserpio enhances the presentation, which can serve as a textbook and as a general reference.