This text is an introduction to topology, covering key concepts such as diffeomorphisms, smooth manifolds, tangent spaces, oriented manifolds, vector fields, ho... » 

This text is an introduction to topology, covering key concepts such as diffeomorphisms, smooth manifolds, tangent spaces, oriented manifolds, vector fields, homotopy, the index number of a map and the Pontryagin construction. Also included are proofs for Sard's theorem and the Hopf theorem. «