  This course has a dual purpose. First we review the successes of the
weak-coupling BCS theory in describing new classes of superconductors
discovered since 1979. They include the heavy-fermion superconductors, high-Tc
cuprate superconductors, organic superconductors, Sr2RuO4, etc. Second, we
present the quasiclassical approximation introduced by Volovik, which we extend
to describe the thermodynamics and the thermal conductivity of the vortex state
in nodal superconductors. This approach provides the most powerful tool to
identify the symmetry of the energy gap function Delta(k) in these new
superconductors.
