  We studied experimentally and theoretically the electronic local density of
states (LDOS) near single step edges at the surface of exfoliated graphite. In
scanning tunneling microscopy measurements, we observed the $(\sqrt{3} \times
\sqrt{3}) R 30^{\circ}$ and honeycomb superstructures extending over 3$-$4 nm
both from the zigzag and armchair edges. Calculations based on a
density-functional derived non-orthogonal tight-binding model show that these
superstructures can coexist if the two types of edges admix each other in real
graphite step edges. Scanning tunneling spectroscopy measurements near the
zigzag edge reveal a clear peak in the LDOS at an energy below the Fermi energy
by 20 meV. No such a peak was observed near the armchair edge. We concluded
that this peak corresponds to the "edge state" theoretically predicted for
graphene ribbons, since a similar prominent LDOS peak due to the edge state is
obtained by the first principles calculations.
