The Resonating Valence Bond theory of the chemical bond was introduced soon
after the discovery of quantum mechanics and has contributed to explain the
role of electron correlation within a particularly simple and intuitive
approach where the chemical bond between two nearby atoms is described by one
or more singlet electron pairs. In this chapter Pauling's resonating valence
bond theory of the chemical bond is revisited within a new formulation,
introduced by P.W. Anderson after the discovery of High-Tc superconductivity.
It is shown that this intuitive picture of electron correlation becomes now
practical and efficient, since it allows us to faithfully exploit the locality
of the electron correlation, and to describe several new phases of matter, such
as Mott insulators, High-Tc superconductors, and spin liquid phases
