The lattice structure of crystals is characterized by specific symmetry properties. Translation symmetry yields the 14 Bravais lattices. Rotation, reflection at a mirror plane, and inversion at a point result in the 32 crystallographic point groups. The diffraction of X-rays by a crystal, initiated in 1912 by Max von Laue, represented the first experimental proof of the regular lattice structure of a crystal. The elements of diffraction theory, including the reciprocal lattice and Brillouin zones, are explained. The chapter ends with a discussion of quasi-crystals and the different types of bonding.