It is well-known that classical invariants of algebraic and differential topology, including smooth fundamental group, smooth singular homology, de Rham cohomology as well as Morse homology, are not sensitive to smooth structures of manifolds but modern physically-based (TQFT) invariants like Donaldson or Seiberg-Witten invariants are so. Thus it seems there should be a deep relation between quantum theory and manifold theory. In this talk, we investigate this relation. Our starting point is that as classical mechanics is not adequate to describe the structures of atoms and we need quantum mechanics to see atoms' structure, classical algebraic and differential topology is not adequate to describe smooth structures of manifolds. In fact, we are going to say that there is a deep analogy between atomic theory and manifold theory and thus the same techniques used in the former can be used in the later. Based on this idea, in this talk, we construct new invariants of smooth structures of the manifold, namely the quantum version of the smooth fundamental group, smooth singular homology, de Rham cohomology as well as Morse homology.