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The book develops a novel approach to perturbative quantum field theory: starting with a perturbative formulation of classical field theory, quantization is done by deformation quantization of the underlying free theory and by the principle that as much as possible from the classical structure has to be maintained The resulting formulation of perturbative quantum field theory is a version of Epstein-Glaser renormalization, which is conceptually clear, mathematically rigorous and pragmatically useful for physicists. The connection to traditional formulations of perturbative quantum field theory is worked out. The formalism is illustrated by a lot of examples and exercises.