Titel: "Faa di Bruno formulae for Green Functions and Cardinality...." Abstract: The classical Faa di Bruno formula expresses the higher derivatives of a composite of two functions in terms of composites of derivatives of the functions. A number of important combinatorial structures arise from the formula, notably the classical Faa di Bruno Hopf algebra. In the context of renormalization of perturbative quantum field theory, van Suijlekom recently discovered that the Green functions that can be defined in the Connes-Kreimer Hopf algebra of Feynman graphs also satisfy a version of the classical Faa di Bruno formula. That result was the first motivation of our work. In this talk we will revise these formulae and will show how the theory of groupoids can be used to give a very conceptual proof of the Faà di Bruno formula for Green functions in the bialgebra of trees. To do so, a thorough study of (homotopy) cardinalities of groupoids is needed. In particular, we show that Green functions are just homotopy cardinalities of certain groupoids, and prove an equivalence of groupoids from which the Faà di Bruno polynomial identity can be recoved on taking the cardinalities of each side.