Introduction The basic theorems

An alternative approach to the orbital theories of the many-electron problem was developed at the same time as these theories [9, 10, 11, 12, 13], it was based on the electron density of the systems considered and reduced the number of degrees of freedom to a minimum, thereby also reducing the computational cost dramatically Unfortunately, this theory lacked in accuracy and was more or less considered a dead end until Hohenberg and Kohn published the article [14] that was to be the start of modern density functional theory. 

density functional theory is the underlying theory behind most solid state calculations, even if traditional wave function methods are still used in smaller systems, where the computational effort is not so big. 

Good texts on the subject are the books by Parr and Wang [8] and Dreizler and Gross [15], and the fabulous online textbook by Burke [16], upon which I have based this chapter. 

---