**The Connes-Moscovici noncommutative index theorem
Walter van Suijlekom
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*Abstract: *We give a panoramic overview of the Connes-Moscovici index formula in noncommutative geometry. It is the generalization of the Atiyah-Singer index theorem to quantum spaces and we try to explain the mathematical preliminaries aiming for a basic understanding of the formula. If time permits, we will sketch its successful application to index computations on the quantum SU(2) group.