Volume A treats crystallographic symmetry in direct or physical space.The first five parts of the volume contain introductory material: lists of symbols and terms; a guide to the use of the space-group tables; the determination of space groups; synoptic tables of space-group symbols; and unit-cell (coordinate) transformations. These are followed by the plane-group and space-group tables.The rest of the volume is at a much higher theoretical level than Parts 1 to 5; it has many features of an advanced textbook of crystallography. Parts 8 to 15 deal with the following aspects of symmetry theory: the mathematical approach to space groups; crystal lattices; point groups and crystal classes; symbols for symmetry operations; symbols for space groups; isomorphic subgroups of space groups; lattice complexes; and normalizers of space groups.Volume A is designed not only for professional crystallographers, but also for chemists, physicists, mineralogists, biologists and material scientists who employ crystallographic methods and who are concerned with the structure and the properties of crystalline materials.