The mathematics of M-theory

String theory, on its modern incarnation M-theory, gives a huge generalization of classical geometry. I indicate how it can be considered as a, two-parameter deformation, where one parameter controls the generalization from points to loops, and the other parameter controls the sum over topologies of Riemaan surfaces. The final mathematical formulation of M-theory will have to make contact with the theory of vector bundles, K-theory and non-commutative geometry.