## ABSTRACT

From the molecular point of view, crystalline substances are assumed to have a discrete, triply periodic structure, the most basic example of which is a (3-dimensional) simple lattice; that is, a set L of points obtained as integral combinations of three independent lattice vectors (see (3.1). As will be discussed in detail in chapter 11, actually most crystals found in nature need to be described by the more complex structures called multilattices, which are ﬁnite collections of translates of a given simple lattice. In many circumstances, however, it is possible to disregard the internal details of the crystalline structure, and describe it as a simple lattice in which the molecular units are regarded as points.1 The notion of a simple lattice is thus central in any theory of crystalline behavior, and is the basis for the study of crystal symmetry which plays a fundamental role in this volume.