We propose to carry out a broad program in nuclear physics research following closely the national priorities determined by the DOE-NSF Nuclear Science Advisory Committee. Much of the research will be carried out with the new RESOLUT rare isotope facility at the Florida State University Superconducting Accelerator Laboratory. This will be directed toward astrophysical studies related to the rapid proton capture process in nucleosynthesis, experimental investigation of the structure of very light nuclei for comparison with forefront ab-initio theoretical calculations, and exploration of how the fundamental shell structure ("magic numbers") in atomic nuclei changes with large proton or neutron excess. Closely related, complementary experiments will also be carried out at the National Superconducting Accelerator Laboratory. The unique FSU polarized lithium beam will also be used to characterize reactions of astrophysical interest. A new type of motion in highly deformed, rapidly rotating nuclei will be explored with Gammasphere at the ATLAS facility. The FSU group constructed a major part of the PHENIX detector at the Relativistic Heavy Ion Collider and now proposes to study the production of J/PSI particles to test how closely the experiments are able to reproduce the quark-gluon plasma that existed in the earliest times of the Big Bang. Other members of the FSU group propose to search for new elementary particles whose unique quantum numbers will clearly prove that they involve excitations of the gluons. Such particles are predicted by the best current models of quarks and gluons, but have not been conclusively seen before. The experiment will be performed at Jefferson Laboratory, which has already approved it with a high rating.