International Tables for Crystallography Volume D: Physical Properties of Crystals is concerned with the influence of symmetry on the physical and tensor properties of crystals and on their structural phase transitions. This role is very important in many different disciplines of the science of materials such as crystallography, elasticity, solid-state physics, magnetism, optics, ferroelectricity and mineralogy. Part 1 introduces the mathematical properties of tensors and of group representations and gives their independent components for each of the crystallographic groups. The software included in the accompanying CD ROM enables the irreducible representations of finite point groups in three dimensions (the 32 crystallographic groups and the groups of the quasicrystalline phases) and the independent components of a tensor of any rank for each of these groups to be determined. Part 2 is devoted to the symmetry aspects of excitations in reciprocal space: phonons, electrons, Raman scattering and Brillouin scattering. Part 3 deals with the symmetry aspects of structural phase transitions and of twinning. A prominent feature is the joint description of twinning and domain structures, which are usually presented in completely separate ways in handbooks of physics and mineralogy. The theory of structural phase transitions relates the symmetry characteristics of the transitions to their physical ones. The application of the symmetry principles that derive from this theory is illustrated by the tables on the CD ROM. The CD ROM also contains tables of tensor properties at any group — subgroup phase transition.