  In this survey, we study representations of finitely generated groups into
Lie groups, focusing on the deformation spaces of convex real projective
structures on closed manifolds and orbifolds, with an excursion on projective
structures on surfaces. We survey the basics of the theory of character
varieties, geometric structures on orbifolds, and Hilbert geometry. The main
examples of finitely generated groups for us will be Fuchsian groups,
3-manifold groups and Coxeter groups.
