The above problem has been open for 70 years now. A foliation on a manifold can be defined in many ways. Perhaps the simplest way is given by an involutive sub-bundle of the tangent bundle of the manifold. The sub-bundle then is integrated into submersed submanifolds of the same dimension that decompose the original manifold. The simplest examples of foliation are principal bundles and fibrations. We will cover the theory of characteristic classes of foliations in three lectures and construct the classes for the codimension one case.