  This article develops a Fermi-liquid theory for superconductors with
anisotropic Fermi surfaces, Fermi-liquid interactions, and energy gaps. For
d-wave superconductors, the Fermi-liquid interaction effects are found to be
classifiable into strong and negligible renormalizaton effects, for symmetric
and antisymmetric combinations of the energies of $k\uparrow$ and
$-k\downarrow$ quasiparticles, respectively. Furthermore, the leading
clean-limit temperature-dependent correction to the superfluid density in a
d-wave superconductor is found to be renormalized by a Fermi velocity (or mass)
renormalization effect. The question is raised of whether or not the
penetration depth in the high temperature superconductor
YBa$_2$Cu$_3$O$_{6+x}a$ can be accounted for with physically acceptable
parameters within the framework of a quasiparticle model. Fermi-liquid
corrections to the spin susceptibility and to the zero-energy
magnetic-field-induced density of states are also evaluated.
