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A generalization of differential operators are pseudodifferential operators which are used for reasoning about partial differential equations with variable coefficients. A lot of useful properties about classical pseudodifferential operators are already discovered by the works of H. Kumano-Go and L. H\"ormander. In this work, we like to transfer their ideas on those operators which symbols are merely H\"older-continous. We focus on the composition of operators, symbol smoothing and operators on manifolds., Comment: thesis, in German