The original approach to Chern classes was via algebraic topology: the Chern classes arise via homotopy theory which provides a mapping associated with a vector bundle to a classifying space (an infinite Grassmannian in this case). For any complex vector bundle "V" over a manifold "M", there exists a map "f" from "M" to the classifying space such that the bundle "V" is equal to the pullback, by "f", of a universal bundle over the classifying space, and the Chern classes of "V" can therefore be defined as the pullback of the Chern classes of the universal bundle. In turn, these universal Chern classes can be explicitly written down in terms of Schubert cycles.