  We review our research work on the single-particle properties and the
equation of state (EOS) of isospin asymmetric nuclear matter within the
framework of the Brueckner-Hartree-Fock (BHF) approach extended by including a
microscopic three-body force (TBF). The TBF is shown to affect significantly
the nuclear matter EOS and the density dependence of nuclear symmetry energy at
high densities above the normal nuclear matter density, and it is necessary for
reproducing the empirical saturation property of symmetric nuclear matter in a
nonrelativistic microscopic framework. The TBF-induced rearrangement effect and
the ground state (g.s.) correlation effect on the s.p. properties in
neutron-rich nuclear matter are investigated. Both effects turn out to be
crucial for predicting reliably the s.p. properties within the Brueckner
framework. The TBF effect on nucleon superfluidity in neutron star matter and
neutron stars has also been discussed.
