In crystal potential, the electronic states form energy bands. In conductors such as metals, the electrons occupy the energy bands up to a certain level. The energy bands and level are called the conduction bands and Fermi level, respectively. The electrons near the Fermi level, which have the highest kinetic energy, dominate the physical properties of the conductors. It is therefore important to know the electronic states in the conduction bands near the Fermi level in order to understand the physical properties of the conductors. The theory to calculate the energy bands in crystals is known as band theoryBand theory. The calculation methods of the energy bands have advanced considerably with the development of computers. In particular, the methods of calculating energy bands without empirical parameters, first-principles calculations, have now been established as a highly effective method for understanding physical properties. In order to provide a straightforward insight into the energy bands, we do not delve into complicated calculations, but instead provide an overview of the band calculations in two limits: the free electron and the tight binding approximationsTight binding approximation. This approach allows for a more comprehensive understanding of how energy bands and the resulting Fermi surfaces are formed.