In the three decades since the introduction of the Kobayashi distance, the subject of hyperbolic complex spaces and holomorphic mappings has grown to be a big industry. This book gives a comprehensive and systematic account on the Carathéodory and Kobayashi distances, hyperbolic complex spaces and holomorphic mappings with geometric methods. A very complete list of references should be useful for prospective researchers in this area. TOC:Introduction.- Distance Geometry.- Schwarz Lemma and Negative Curvature.- Intrinsic Distances.- Intrinsic Distances for Domains.- Holomorphic Maps into Hyperbolic Spaces.- Extension and Finiteness Theorems.- Manifolds of General Type.- Value Distributions.- References.- Index.- Logarithmic Geometry.
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