  Physicists believe, with some justification, that there should be a
correspondence between familiar properties of Newtonian gravity and properties
of solutions of the Einstein equations. The Positive Mass Theorem (PMT), first
proved over twenty years ago \cite{SchoenYau79b,Witten81}, is a remarkable
testament to this faith. However, fundamental mathematical questions concerning
mass in general relativity remain, associated with the definition and
properties of quasi-local mass. Central themes are the structure of metrics
with non-negative scalar curvature, and the role played by minimal area
2-spheres (black holes).
