  Significant progress has been made in recent years in constraining nuclear
symmetry energy at and below the saturation density of nuclear matter using
data from both terrestrial nuclear experiments and astrophysical observations.
However, many interesting questions remain to be studied especially at
supra-saturation densities. In this lecture note, after a brief summary of the
currently available constraints on nuclear symmetry energy near the saturation
density we first discuss the relationship between the symmetry energy and the
isopin and momentum dependence of the single-nucleon potential in
isospin-asymmetric nuclear medium. We then discuss several open issues
regarding effects of the tensor force induced neutron-proton short-range
correlation (SRC) on nuclear symmetry energy. Finally, as an example of the
impacts of nuclear symmetry energy on properties of neutron stars and
gravitational waves, we illustrate effects of the high-density symmetry energy
on the tidal polarizability of neutron stars in coalescing binaries.
