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We shall introduce the cyclic cohomology (of algebras) to study the characteristic classes of the leaf spaces of foliations, as a quantum (or non-commutative) counterpart of the de Rham cohomology (of smooth manifolds) to study the characteristic invariants of manifolds. We next discuss a few examples of quantum groups, as well as their actions on algebras, and we present the Hopf-cyclic cohomology as a computational tool for the cyclic cohomology of algebras. Time permitting, we shall illustrate an explicit computation or two.