  After explaining the motivation for this article, I briefly recapitulate the
methods used to determine, somewhat coarsely, the rotation curves of our Milky
Way Galaxy and other spiral galaxies, especially in their outer parts, and the
results of applying these methods. Recent observations and models of the very
inner central parts of galaxian rotation curves are only briefly described. I
then present the essential Newtonian theory of (disk) galaxy rotation curves.
The next two sections present two numerical simulation schemes and brief
results. Application of modified Newtonian dynamics to the outer parts of disk
galaxies is then described. Finally, attempts to apply Einsteinian general
relativity to the dynamics are summarized. The article ends with a summary and
prospects for further work in this area.
