  We extend the Fermi-liquid (FL) theory to include spin-orbit (SO) splitting
of the energy bands, focusing on the Rashba SO coupling as an example. We
construct the phenomenological Landau interaction function for such a system
using the symmetry arguments and verify this construction by an explicit
perturbative calculation. The Landau function is used to obtain the effective
mass, compressibility, and stability conditions of the FL. It is shown that
although the charge-sector properties, such as the effective mass and
compressibility, are determined solely by well-defined quasiparticles, the
spin-sector properties, such as the spin susceptibility, contain a contribution
from damped states in between the spin-split Fermi surfaces, and thus cannot be
fully described by the FL theory, except for the case of weak SO coupling. We
derive some specific properties of a chiral FL and show, in particular, that
for contact interaction spin-splitting of the Fermi velocities of Rashba
subbands occurs because of the Kohn anomaly, also modified by SO coupling.
