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

Origins and Impacts of High-Density Symmetry Energy