  Grafting is a surgery on Riemann surfaces introduced by Thurston which
connects hyperbolic geometry and the theory of projective structures on
surfaces. We will discuss the space of projective structures in terms of the
Thurston's geometric parametrization given by grafting. From this approach we
will prove that on any compact Riemann surface with genus greater than $1$
there exist infinitely many projective structures with Fuchsian holonomy
representations. In course of the proof it will turn out that grafting is
closely related to harmonic maps between surfaces.
