  The adiabatic invariant nature of black hole horizon area in classical
gravity suggests that in quantum theory the corresponding operator has a
discrete spectrum. I here develop further an algebraic approach to black hole
quantization which starts from very elementary assumptions, and proceeds by
exploiting symmetry. It predicts a uniformly spaced area spectrum for all
charges and angular momenta. Area eigenvalues are degenerate; correspondence
with black hole entropy then dictates a precise value for the interval between
eigenvalues.
