  The aim of the note is to provide an introduction to the algebraic, geometric
and quantum field theoretic ideas that lie behind the
Kontsevich-Cattaneo-Felder formula for the quantization of Poisson structures.
We show how the quantization formula itself naturally arises when one imposes
the following two requirements to a Feynman integral: on the one side it has to
reproduce the given Poisson structure as the first order term of its
perturbative expansion; on the other side its three-point functions should
describe an associative algebra. It is further shown how the Magri-Koszul
brackets on 1-forms naturally fits into the theory of the Poisson sigma-model.
