This brings us to the end of our introduction to numerical relativity. A quick glance at the table of contents shows that we have covered a wide range of subjects, starting with the foundations of numerical relativity and continuing with applications to different areas of gravitational physics and astrophysics. Despite the breadth of our survey, we have had to be selective in our choice of topics. Our focus has been on solving the Cauchy problem in general relativity for dynamical, asymptotically flat spacetimes, with applications to compact objects and compact binaries. There are a number of alternative approaches for solving Einstein's equations that we did not touch on at all, such as the characteristic approach and the Regge calculus. We also did not discuss in any detail applications involving strictly stationary spacetimes, such as gas accretion onto Kerr black holes, although some of the same schemes we described for matter evolution have been used successfully to treat problems with fixed background metrics.We trust that interested readers will find discussions of the subjects we omitted elsewhere in the literature.

We hope that our treatment laying out the foundations of numerical relativity will remain relevant for the foreseeable future. However, we suspect that some of the large-scale simulations we have chosen to illustrate different implementations will be superseded by more sophisticated calculations.