Preface.- German letters.- The rank of a holomorphic map.- Product representations.- Meromorphic functions.- Dependence.- Proper, light, holomorphic maps.- The field .- Semi-proper maps.- Quasi-proper maps.- as a finite algebraic extension of .- Quasi-proper maps of codimension k.- Full holomorphic maps.- Globalization.- The schwarz Lemma.- Sections in meromorphic line bundles.- Preparations.- Pseudoconcave maps.- A counter example by Kas.