Fermi Liquid Theory
Landau's idea of a "Fermi liquid": the state of electrons in a real metal is adiabatically connected to the free Fermi gas, in the same way as a liquid can be adiabatically connected (at high temperature and pressure, say, above the boiling transition) to a gas. There is no fundamental difference in symmetry between a metal and a Fermi gas, but there may be major differences in quantities such as the electron effective mass as a result of strong electron-electron interactions.
The first approach to Fermi liquid theory is as a phenomenology introduced by Landau and Silin that allows for strong interactions to be captured in a set of parameters that control experimental quantities. Later approaches, based on renormalization group for example (see a Reviews of Modern Physics article by R. Shankar) attempted to give some understanding for why the Fermi liquid is unstable to some types of perturbations in some dimensions (e.g., attractive interactions give superconductivity; even repulsive interactions lead to a different phase in one spatial dimension) but can be very stable to ordinary repulsive interactions.