  In this lecture we argue that the fluctuations of Dirac eigenvalues on the
finest scale, i.e. on the scale of the average level spacing do not depend on
the underlying dynamics and can be obtained from a chiral random matrix theory
with the same low energy effective theory. We present three pieces of evidence
supporting that such microscopic correlations of lattice QCD Dirac spectra are
given by chiral random matrix theory. First, we find that the spectral
correlations of eigenvalues in the bulk of the spectrum obey the
Dyson-Mehta-Wigner statistics. Second, we show that the valence quark mass
dependence for sufficiently small quark masses, as calculated by the Columbia
group, can be obtained from the microscopic spectral density of chiral random
matrix theory. Third, in the framework of chiral random matrix models, we
present results showing that the microscopic spectral density is strongly
universal, i.e. is insensitive to the details of the probability distribution.
