Affine differential geometry -- Riemannian curvature -- Flat Riemannian manifolds -- Representations of finite groups -- Vincent's work on the spherical space form problem -- The classification of fixed point free groups -- The solution to the spherical space form problem -- Rieman symmetric spaces -- Space forms of irreducible symmetric spaces -- Locally symmetric spaces of non-negative curvature -- Spaces of constant curvature -- Locally isotropic manifolds