This research is focused on understanding the strong-field regime of Einstein's theory of general relativity. This encompasses both observational and theoretical aspects of general relativity. On the observational side, the main effort is numerical simulations of black hole collisions. This is important to support the nascent field of gravitational wave astronomy that began in 2015 with LIGO's detection of the collision of two black holes. This has given us the first direct observational window into the strong-field regime of general relativity, showing tentative scientific evidence that space and time do behave as predicted in these extreme environments. One avenue of work supported by this award will be to investigate hypothetical alternatives to black hole mergers as the source of LIGO's observations, to either rule out the alternatives and improve our confidence in general relativity or to discover novel physics. On the theoretical side, there are many outstanding questions about the nature of spacetime in extreme situations. Two such questions that will be addressed through this award are what happens to a black hole that is spun up to the maximum rotation rate allowed by Einstein's theory, and what happens when two black holes traveling at close to the speed of light collide. The pursuit of these projects will be carried out by graduate students as part of their thesis work. They will be trained to do leading scientific research, become knowledgeable in correspondin