  The microscopic calculation of nuclear level densities in the presence of
correlations is a difficult many-body problem. The shell model Monte Carlo
method provides a powerful technique to carry out such calculations using the
framework of the configuration-interaction shell model in spaces that are many
orders of magnitude larger than spaces that can be treated by conventional
methods. We present recent applications of the method to the calculation of
level densities and their collective enhancement factors in heavy nuclei. The
calculated level densities are in close agreement with experimental data.
