Research in theoretical physics and astrophysics uses advances in theoretical physics to understand how nature works. Specifically, this project uses quantum mechanics applied in the context of exotic environments provided by collapsing stars and the very early universe, to glean new insights into the fundamental properties and behaviors of elementary particles and of atomic nuclei. The calculations performed here go the other way as well, using what is known about elementary particles and atomic nuclei to understand the cosmos. Experiments and observations have revealed that roughly 95% of the mass and energy in the universe is not explained by ordinary atoms. That staggering fact demands investigation on many fronts. To that end, the research made possible by this project focuses on the properties and behavior of one particularly mysterious elementary particle, the neutrino. The objective is twofold: (1) Better understanding of how these particles interact with atomic nuclei and affect the evolution of the early universe, the collapse of massive stars, and associated production of elements and black holes; and (2) Use those particles as a portal to new and unknown physics. The calculations in this research are pioneering new approaches to treating complex quantum problems. They serve to train the next generation of physicists and astrophysicists. This theoretical research revolves around calculations of neutrino interactions, the weak interaction, and the structure of a