The relative abundances of atomic nuclei, and thus the elements found in nature, require production mechanisms in extreme environments, such as those present during the Big Bang in the early universe and inside stars. One cannot create such conditions in laboratories. However, using theoretical methods, one can extrapolate terrestrial measurements to astrophysically-relevant densities and temperatures. The list of atomic nuclei, many of them short-lived, is in the thousands and nuclear theory plays a crucial role in analyzing the properties of known nuclei from measurements. In this broader picture, this project develops and applies the effective field theory (EFT) formalism to calculate several reaction rates central to the understanding of the stars' evolution, including our Sun. Key reactions for understanding the abundances of life-giving oxygen and carbon in stellar synthesis will be studied. Solar reactions that help probe physics beyond the Standard Model of particle physics will also be calculated with high precision. In addition, lattice EFT method for exact numerical calculations will be developed. The broader impacts of this research include training graduate students in nuclear physics, as well as in numerical and analytical work, for an academic or industry career that benefits society. This project builds on past work by the PI and his collaborators on halo nuclei and lattice EFT. Halo nuclei have excess protons or neutrons that form a halo around a core. T