Following earlier treatments of charged quasiparticles in semiconductors, this chapter develops the concept of phonons, i.e., quanta of lattice vibrations. Based on the interatomic potential, harmonic oscillations of the atoms in a crystal are discussed, as are anharmonic effects such as thermal expansion. Dispersion relations are derived for one-atom and two-atom linear chain models, resulting in an understanding of the acoustic and optical branches, speed of sound, and lattice vibrations in the form of standing waves. The dispersion relations of one-dimensional chains of atoms are then generalized to account for the phonon dispersion in three-dimensional crystals. Finally, phonons as quanta of lattice vibrations are formally introduced, and conservation laws are established that govern their interaction with charge carriers in semiconductors.