  Classical black holes are defined by the property that things can go in, but
don't come out. However, Stephen Hawking calculated that black holes actually
radiate quantum mechanical particles. The two important ingredients that result
in back hole evaporation are (1) the spacetime geometry, in particular the
black hole horizon, and (2) the fact that the notion of a "particle" is not an
invariant concept in quantum field theory. These notes contain a step-by-step
presentation of Hawking's calculation. We review portions of quantum field
theory in curved spacetime and basic results about static black hole
geometries, so that the discussion is self-contained. Calculations are
presented for quantum particle production for an accelerated observer in flat
spacetime, a black hole which forms from gravitational collapse, an eternal
Schwarzschild black hole, and charged black holes in asymptotically deSitter
spacetimes. The presentation highlights the similarities in all these
calculations. Hawking radiation from black holes also points to a profound
connection between black hole dynamics and classical thermodynamics. A theory
of quantum gravity must predicting and explain black hole thermodynamics. We
briefly discuss these issues and point out a connection between black hole
evaportaion and the positive mass theorems in general relativity.
