Analytic and Algebraic Dependence of Meromorphic Functions 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.