Christian Ratsch Institute for Pure and Applied Mathematics IPAM Associate Director In this talk, I will discuss the basic concepts for electronic structure calculations for periodic systems. I will discuss the definition of the primitive cell and the Wigner-Seitz cell in real space. I will then discuss periodicity in the reciprocal space, and discuss the concept of the Brillouin zone. The physical origin of a bandstructure in solids and the Bloch theorem will be discussed. In the second part of the talk, I will introduce the supercell approach, and how supercells can be used to treat systems with a defect. Examples for diffusion on a surface, and the calculation of surface energies will be given.