  What is nuclear symmetry energy? Why is it important? What do we know about
it? Why is it so uncertain especially at high densities? Can the total symmetry
energy or its kinetic part be negative? What are the effects of three-body
and/or tensor force on symmetry energy? How can we probe the density dependence
of nuclear symmetry energy with terrestrial nuclear experiments? What
observables of heavy-ion reactions are sensitive to the high-density behavior
of nuclear symmetry energy? How does the symmetry energy affect properties of
neutron stars, gravitational waves and our understanding about the nature of
strong-field gravity? In this lecture, we try to answer these questions as best
as we can based on some of our recent work and/or understanding of research
done by others. This note summarizes the main points of the lecture.
