The property which distinguishes semiconductors from other materials concerns the behavior of their electrons, in particular the existence of gaps in their electronic excitation spectra. The microscopic behavior of electrons in a solid is most conveniently specified in terms of the electronic band structure. The purpose of this chapter is to study the band structure of the most common semiconductors, namely, Si, Ge, and related III– V compounds. We will begin with a quick introduction to the quantum mechanics of electrons in a crystalline solid.