In the talk I will introduce a new form of K-theory.It will be based on bundles of 2-vector-spaces in the sense of Kapranov and Voevodsky. By techniques from algebraic K-theory we can show that this new cohomolgy theory is represented by the spectrum K(ku). This is of chromatic filtration two and therefore the new theory gives a geometric, bundle like model of a form of elliptic cohomology.This has been asked for over a long time. I will motivate the construction from ideas in topological quantum field theory. This leads to a whole new programme which I call "Higher Order Topology" - the use of higher categories to pick up new topological information. This is joint work with B.I. Dundas and J.Rognes - work still in progress. Some of the material is in: N.A.Baas,B.I.Dundas and J.Rognes:Two-vector bundles and forms of elliptic cohomology (to appear in the Proc. of the Segal Conf., Oxford- June 2002).