  The random first order transition theory of the dynamics of supercooled
liquids is extended to treat aging phenomena in nonequilibrium structural
glasses. A reformulation of the idea of ``entropic droplets'' in terms of
libraries of local energy landscapes is introduced which treats in a uniform
way the supercooled liquid (reproducing earlier results) and glassy regimes.
The resulting microscopic theory of aging makes contact with the
Nayaranaswamy-Moynihan-Tool nonlinear relaxation formalism and the
Hodge-Scherer extrapolation of the Adam-Gibbs formula, but deviations from both
approaches are predicted and shown to be consistent with experiment. The
nonlinearity of glassy relaxation is shown to quantitatively correlate with
liquid fragility. The residual nonArrhenius temperature dependence of
relaxation observed in quenched glasses is explained. The broadening of
relaxation spectra in the nonequilibrium glass with decreasing temperature is
quantitatively predicted. The theory leads to the prediction of spatially
fluctuating fictive temperatures in the long-aged glassy state, which have
non-Gaussian statistics. This can give rise to ``ultra-slow'' relaxations in
systems after deep quenches.
