Lectures on the Automorphism Groups of Kobayashi Hyperbolic Manifolds The Homogeneous Case The Case d(M) = n2 The Case d(M) = n2 1 n  3 The Case of (2 3) Manifolds Proper Actions. Kobayashi hyperbolic manifolds are an object of active research in complex geometry. In this monograph the author presents a coherent exposition of recent results on complete characterization of Kobayashi hyperbolic manifolds with high dimensional groups of holomorphic automorphisms. These classification results can be viewed as complex geometric analogues of those known for Riemannian manifolds with high dimensional isotropy groups that were extensively studied in the 1950s 70s. The common feature of the Kobayashi hyperbolic and Riemannian cases is the properness of the actions of the holomorphic automorphism group and the isometry group on respective manifolds.