  We study the subgap spectrum of a 2D Abrikosov vortex in an s-wave
superconductor in the absence and presence of a point impurity. By solving the
Eilenberger equations without impurity for two models of the vortex (including
a self-consistent one), we find multiple subgap spectral branches. The number
of these branches may be arbitrary large provided that the magnetic field
screening length is large enough. The quasiclassical spectrum of the vortex has
a local gap with a width of the order of the bulk gap and a spatial extent of
several coherence lengths. The existence of such gap is the prerequisite for
the appearance of discrete impurity-induced states. Within the Gor'kov
equations formalism, we find that a single impurity induces up to four discrete
quasiparticle states in the vortex. The energies and wavefunctions of the
impurity states are calculated for different parameters. We claim that most of
the predicted spectral features can be observed in scanning tunnel spectroscopy
experiments.
