**1. Introduction**

The study of the microscopic properties of a physical system in the condensed matter branch requires the solution of the Schrödinger equation. When the studied system is composed of a large number of interacting atoms, the analytical solution of the Schrödinger equation becomes impossible. However, certain numerical calculation methods provide access to a solution to this fundamental equation for increasingly large systems. The calculation methods, called ab-initio like the density functional theory (DFT), propose to solve the Schrödinger equation without adjustable parameters. The density functional theory quickly established itself as a relatively fast and reliable way to simulate electronic and structural properties for all of the elements of the periodic table ranging from molecules to crystals. In this chapter, we recall the principle of this theory which considers electron density as a fundamental variable and that all physical properties can be expressed as a function of it.
