  We establish a moderate deviation principle (MDP) for the number of
eigenvalues of a Wigner matrix in an interval close to the edge of the
spectrum. Moreover we prove a MDP for the $i$th largest eigenvalue close to the
edge. The proof relies on fine asymptotics of the variance of the eigenvalue
counting function of GUE matrices due to Gustavsson. The extension to large
families of Wigner matrices is based on the Tao and Vu Four Moment Theorem.
Possible extensions to other random matrix ensembles are commented.
