This chapter provides an introduction to the discussion on the structure of ideal surfaces. A lattice is a three-dimensional array of points in space such that every point has the same environment of lattice points in the same orientation. An ideal crystal consists of an array of identical atomic motifs, one located at each point of a lattice. An ideal half-crystal is formed by dividing an ideal crystal by a plane and removing all atoms on one side of the plane without moving the other atoms from their original positions. A surface atom is an atom in a half-crystal whose properties differentiate it from an atom of the same class in an ideal crystal.