Title: Some aspects of holomorphic mappings: a survey,
Abstract: This expository paper is concerned with the properties of proper holomorphic
mappings between domains in complex affine spaces. We discuss some of the main
geometric methods of this theory, such as the Reflection Principle, the scaling
method, and the Kobayashi-Royden metric. We sketch the proofs of certain
principal results and discuss some recent achievements. Several open problems
are also stated.