While there is a consensus in the astronomical community that most of the mass of our Galaxy and of most galaxies is in the form of some non-luminous matter , there is only speculation about its nature.
In his lecture, Charles Alcock (see the contribution by C. Alcock to these proceedings) presents a report of recent progress in efforts to detect baryonic dark matter. Here, I will focus on non-baryonic dark matter.
I will begin by presenting three arguments that suggest that the dark matter is non-baryonic. None of these arguments are definitive. John Bahcall has urged the speakers to identify interesting problems for graduate students. In addition to the grand challenge of detecting the dark matter, I believe that an easier problem is to make some of the arguments for dark matter more compelling.