Introduction Part I. Geometry, distances, and measures on $B̂n$ 1. The automorphism group of $B̂n$ 2. Invariant distances on $B̂n$ 3. Measures and dimension on $B̂n$ 4. Hyperbolic measure on $B̂n$ 5. Invariant Hausdorff measure on $B̂n$ Appendix to Part I Part II. Intrinsic measures on complex manifolds 1. $\kappa $ and $\gamma $ measures 2. Measures defined by integrals: $\Gamma ̂k_n$ and $\mathrm {K}̂k_n$ 3. Relations to distances Part III. Applications to the study of holomorphic mappings 1. General results 2. A generalization of Huber's theorem
