  These lectures discuss an S-matrix approach to quantum gravity, and its
relation to more local spacetime approaches. Prominent among the problems of
quantum gravity are those of unitarity and observables. In a unitary theory
with solutions approximating Minkowski space, the S-matrix (or, in four
dimensions, related inclusive probabilities) should be sharply formulated and
physical. Features of its perturbative description are reviewed. A successful
quantum gravity theory should in particular address the questions posed by the
ultrahigh-energy regime. Some control can be gained in this regime by varying
the impact parameter as well as the collision energy. However, with decreasing
impact parameter gravity becomes strong, first eikonalizing, and then entering
the regime where in the classical approximation black holes form. Here one
confronts what may be the most profound problem of quantum gravity, that of
providing unitary amplitudes, as seen through the information problem of black
hole evaporation. Existing approaches to quantum gravity leave a number of
unanswered questions in this regime; there are strong indications that new
principles and mechanisms are needed, and in particular there is a good case
that usual notions of locality are inaccurate. One approach to these questions
is investigation of the approximate local dynamics of spacetime, its
observables, and its limitations; another is to directly explore properties of
the gravitational S-matrix, such as analyticity, crossing, and others implied
by gravitational physics.
