Lectures on differential topology

In a differential topology textbook for beginning graduate students who have finished a standard undergraduate mathematics curriculum, Benedetti introduces the theory of smooth manifolds, maps, and associated fundamental structures with an emphasis on "bare hands" approaches that combine differential-topology cut-and-paste procedures and applications of transversality. In particular, he defines the smooth cobordism cup-product from scratch and uses it as the main tool in a variety of settings. The book can serve as a source of alternative constructive approaches to results commonly presented in more advanced contexts with specialized techniques.