  The equation of state (EoS) of neutron star matter, constrained by the
existence of two-solar-mass stars and gravitational wave signals from neutron
star mergers, is analysed using the Landau theory of relativistic Fermi
liquids. While the phase diagram of dense and cold QCD matter is still open for
scenarios ranging from hadronic to quark matter in the center of neutron stars,
a Fermi-liquid treatment is motivated by a microscopic approach starting from a
chiral nucleon-meson field theory combined with nonperturbative functional
renormalization group methods. In this scheme effects of multipionic
fluctuations and repulsive nuclear many-body correlations suggest that the
transition to chiral symmetry restoration is shifted to densities above those
typically encountered in the neutron star core. Under such conditions a
Fermi-liquid description in terms of nucleon quasiparticles appears to be
justified. The leading Landau parameters are derived and discussed. Our results
are contrasted with a well-known Fermi liquid, namely liquid $^3$He.
