  The modern form of the Moments Method applied to the calculation of the
nuclear shell-model level density is explained and examples of the method at
work are given. The calculated level density practically exactly coincides with
the result of full diagonalization when the latter is feasible. The method
provides the pure level density for given spin and parity with spurious
center-of-mass excitations subtracted. The presence and interplay of all
correlations leads to the results different from those obtained by the
mean-field combinatorics.
