International Tables for Crystallography is the definitive resource and reference work for crystallography and structural science. Each of the eight volumes in the series contains articles and tables of data relevant to crystallographic research and to applications of crystallographic methods in all sciences concerned with the structure and properties of materials. Emphasis is given to symmetry, diffraction methods and techniques of crystal-structure determination, and the physical and chemical properties of crystals. The data are accompanied by discussions of theory, practical explanations and examples, all of which are useful for teaching. Volume A treats crystallographic symmetry in direct or physical space. It contains extensive tabulations and illustrations of the 17 plane groups, the 230 space groups and the 32 crystallographic point groups. Parts 1-5 of the volume present introductory material, including lists of symbols and terms, a guide to the use of the space-group tables, and the determination of space groups. Later parts discuss aspects of symmetry theory, such as crystal lattices and normalizers of space groups. Thoroughly updated and improved, the latest edition of Volume A includes an additional chapter on further properties of lattices.