  We review the chiral variant and invariant components of nucleon masses and
its consequence on the chiral restoration in extreme conditions, neutron star
matter in particular. We consider a model of linear realization of chiral
symmetry with the nucleon parity doublet structure that permits the chiral
invariant mass, $m_0$, for positive and negative parity nucleons. Nuclear
matter is constructed with the parity doublet nucleon model coupled to scalar
fields $\sigma$, vector fields $(\omega, \rho)$, and to mesons with strangeness
through the U(1)$_A$ anomaly. In models with large $m_0$, the nucleon mass is
insensitive to the medium, and the nuclear saturation properties can be
reproduced without demanding strong couplings of nucleons to scalar fields
$\sigma$ and vector fields $\omega$. We confront the resulting nuclear
equations of state with nuclear constraints and neutron star observations, and
delineate the chiral invariant mass and effective interactions. To further
examine nuclear equations of state beyond the saturation density, we supplement
quark models to set the boundary conditions from the high density side. The
quark models are constrained by the two-solar mass conditions, and such
constraints are transferred to nuclear models through the causality and
thermodynamic stability conditions. We also calculate various condensates and
matter composition from nuclear to quark matter in a unified matter, by
constructing a generating functional that interpolates nuclear and quark matter
with external fields. Two types of chiral restoration are discussed; the one
due to the positive scalar charges of nucleons, and the other triggered by the
evolution of the Dirac sea. We found the U(1)$_A$ anomaly softens equations of
state from low to high density.
