After a cursory review of the concept of elasticity, while keeping in mind the motivation of the previous chapter, a definition of the material symmetry group at a point of an elastic body is formulated. For the sake of completeness, some basic notions of the mechanics of continuous media are reviewed and discussed, including a characterization of some elastic materials properties (such as fluidity, solidity, isotropy, orthotropy) according to the corresponding symmetry groups. The material symmetry group is a strictly local concept at each point of the body. The comparison of pairs of different points gives rise to the idea of the material groupoid. Two points made of the same material are said to be materially isomorphic. Material isomorphism can thus be regarded as a distant symmetry. A body all whose points are mutually materially isomorphic is said to be materially uniform.