Abstract: In this thesis we construct explicit formulae for characteristic classes in noncommutative geometry. The general framework for the construction of characteristic classes in Noncommutative geometry is provided by Connes' theory of cycles and their characters. We first consider the case of generalized cycles with "curvature" and define characters for them. We prove that our definition agrees with Connes' original definition. We then proceed to apply our construction to several geometric situations. We treat the case of vector bundles on manifolds, equivariant with respect to the action of discrete group, and the case of holonomy equivariant vector bundle on a foliated manifold, and discuss relation of our construction to Connes' construction of the Godbillon-Vey cocycle. We also derive formulae for the Chern character of finitely summable Fredholm module, as well as transgression formulae. Finally we discuss a different approach to the characteristic classes, using the cyclic analogue of the Paschke-Voiculescu duality.