  We define convex projective structures on 2D surfaces with holes and
investigate their moduli space. We prove that this moduli space is canonically
identified with the higher Teichmuller space for the group PSL_3 defined in our
paper math/0311149. We define the quantum version of the moduli space of convex
projective structures on surfaces with holes. The present paper can serve as an
introduction to math/0311149. In the Appendix we show that the space of
configurations of 5 flags in the projective plane is of cluster type E_7.
