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These lectures are devoted to a description of anomalies in quantum field theory from the point of view of noncommutative geometry and topology. We will in particular introduce the basic methods of cyclic cohomology and explain the noncommutative counterparts of the Atiyah-Singer index theorem.doi:10.1090/conm/434/08344 fatcat:4t6qspw57bfxzbk4cfafc256ma