Physical and mathematic presentation of material properties and their relation to the symmetry of crystals; ceramics; glasses; and isotropic materials. Presentation of properties in both matrix and tensor forms. Properties include linear and non-linear equilibrium properties (e.g.; permittivity; stiffness; permeability; piezoelectricity; electro-optic and magneto-optic) and transport properties (e.g.; diffusivity; electrical conductivity). Inter-relationship of properties using Maxwell Relations and thermodynamics.