These lectures present the Fermi-liquid theory of superconductivity, which is applicable to a broad range of systems that are candidates for non-s wave pairing, e.g. the heavy fermions, organic metals and the CuO superconductors. Ginzburg-Landau (GL) theory provides an important link between experimental properties of non-s wave superconductors and the more general Fermi-liquid theory. The multiple superconducting phases of UPt3 provide an ideal example of the role that is played by the GL theory for non-s-wave superconductors. The difference between non-s wave superconductivity and conventional anisotropic superconductivity is illustrated here by the unique effects that impurities are predicted to have on the properties of non-s wave superconductors.