Given a compact manifold which admits at least one hyperbolic metric, one =can ask the following question: How many different hyperbolic metrics can I put on the manifold? It turns out that a surface of genus greater than or equal to 2 admits uncountably many distinct hyperbolic metrics, and Teichmuller space is simply a parametrization of these metrics. The answer in dimension greater that or equal to 3 (provided by Mostow) is striking: We can put at most one hyperbolic metric on a manifold. More specifically, homotopy equivalent hyperbolic n-manifolds (n>=3) are isometric.