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Differential topology Lecture notes (PDF 20p)
This note covers the following topics: Smooth manifolds and smooth maps, Tangent spaces and differentials , Regular and singular values , Manifolds with boundary, Immersions and embeddings , Degree mod 2 , Orientation of manifolds and Applications of degree.
Author(s): Sergei Tabachnikov
20 Pages 
Differential Topology by Andrew Kobin
This note covers Smooth manifolds, Regular values, Transversality and embeddings, Vector bundles.
Author(s): Andrew Kobin
52 Pages
Topics in Differential Topology by Mohammad F Tehrani
This note explains the following topics: preliminaries, Different homology theories and their interaction, Classifying spaces, An introduction to symplectic topology.
Author(s): Mohammad F Tehrani
104 Pages
Introduction to Differential Topology by Uwe Kaiser
This book gives a deeper account of basic ideas of differential topology than usual in introductory texts. Also many more examples of manifolds like matrix groups and Grassmannians are worked out in detail. Topics covered includes: Continuity, compactness and connectedness, Smooth manifolds and maps, Regular values and Sards theorem, Manifolds with boundary and orientations, Smooth homotopy and vector bundles, Intersection numbers, vector fields and Euler characteristic.
Author(s): Uwe Kaiser
110 Pages
Introduction To Differential Topology
The first half of the book deals with degree theory, the Pontryagin construction, intersection theory, and Lefschetz numbers. The second half of the book is devoted to differential forms and deRham cohomology.
Author(s): Joel W. Robbin and Dietmar A. Salamon
306 Pages