This project will create a Theoretical and Computational Astrophysics Network with major nodes at the California Institute of Technology, Syracuse University, Cornell University, and the University of Washington to advance the theory of merging compact-object binaries and stellar collapse. Gravitational waves from these types of events are expected to be detected by the Advanced Laser Interferometer Gravitational Wave Observatory in coming years. The network team’s goals are to develop the theoretical and computational tools needed to extract the equation of state of dense nuclear matter from gravitational wave and electromagnetic observations, and to determine the impact of compact-object mergers on the synthesis of light and heavy elements. The team will combine its expertise in numerical relativity, nuclear astrophysics, and gravitational wave detection to (1) develop an open-source, next-generation relativistic astrophysics computation framework; (2) improve the theoretical understanding of the nuclear equation of state and compute a large ensemble of equations of state for different temperatures and compositions; (3) improve the computational treatment of nuclear reactions in merger and collapse simulations; and (4) develop parameter estimation techniques to extract information on the equation of state from multi-messenger observations. The network will contribute to scientific workforce development through the involvement of graduate students and postdocs, who will receive cross-disciplinary training in modeling, microphysics, and multi-messenger observations. Outreach videos with visualizations and interviews with project scientists will be disseminated via YouTube to enhance public understanding.