When dealing with transition metal compounds one has to look at the different degrees of freedom involved and their interplay. These degrees of freedom are charge, spin, and orbitals. And of course all electronic phenomena occur on the background of the lattice, that is one always has to think about the role of the interaction with the lattice, or with phonons.

The electron spins are responsible for different types of magnetic ordering. The orbitals, especially in the case of orbital (or Jahn—Teller) degeneracy, also lead to a particular type of ordering, and the type of orbital occupation largely determines the character of magnetic exchange and of the resulting magnetic structures.

As to charges, the first question to ask is whether the electrons have to be treated as localized or itinerant. We actually started this book by discussing two possible cases: a band description of electrons in solids, in which the electrons are treated as delocalized, and the picture of Mott insulators, with localized electrons.

But even for localized electrons there still exists some freedom, which has to do with charges. In some systems charges may be disordered in one state, for example at high temperatures, and become ordered at low temperatures. This charge ordering (CO) will be the main topic of this chapter. But, to put it in perspective, we will start by discussing different possible types of ordering, connected with charge degrees of freedom.