Differential topology is the study of smooth manifolds, which are generalizations of curves and surfaces in space. The course begins with a rapid  introduction to point-set topology, then a review of tools from multivariable real analysis. The main topics of the course include definition and construction of smooth manifolds, tangent spaces, vector fields and flows, neighborhood theorems, and transversality. Additional topics may include degree theory, intersection theory, and differential forms on manifolds.