A theoretical study of the dynamics and stability of extrasolar planetary systems will be conducted. The overall goal is a better understanding of the formation and evolution of planetary systems around other stars, particularly those in extreme environments. Special emphasis will be placed on multiple planet systems, systems during stellar interactions, pulsar planet systems, and interactions between planetary dynamics and the central star. Central to this work is the combination of orbital dynamics and hydrodynamic methods in the simulations, as well as stellar evolution where appropriate. Planned improvements include removing approximations in gravitational scattering and better treatments of tides and tidal heating (among others). The dynamics simulation tools developed here will also have application to many broader areas of astrophysics. The work here is part of a student-oriented research program in computational astrophysics which will be continued. A postdoctoral fellow will be supported and trained in numerical modeling as well. The resulting animations will also be incorporated into public exhibitions and activities at the nearby Adler Planetarium.