Introduction Chapter 1 Manifolds and Maps 0.Submanifolds of Rn+k 1.Differential Structures 2.Differentiable Maps and the Tangent Bundle 3.Embeddings and Immersions 4.Manifolds with Boundary 5.A Convention Chapter 2 Function Spaces 1.The Weak and Strong Topologies on C'(M,N) 2.Approximations 3.Approximations on 0-Manifolds and Manifold Pairs 4.Jets and the Baire Property 5.Analytic Approximations Chapter 3 Transversality 1.The Morse-Sard Theorem 2.Transversality Chapter 4 Vector Bundles and Tubular Neighborhoods 1.Vector Bundles 2.Constructions with Vector Bundles 3.The Classification of Vector Bundles 4.Oriented Vector Bundles 5.Tubular Neighborhoods 6.Collars and Tubular Neighborhoods of Neat Submanifolds 7.Analytic Differential Structures Chapter 5 Degrees, Intersection Numbers,and the Euler Characteristic 1.Degrees of Maps 2.Intersection Numbers and the Euler Characteristic 3.Historical Remarks Chapter 6 Morse Theory 1.Morse Functions 2.Differential Equations and Regular Level Surfaces 3.Passing Critical Levels and Attaching Cells 4.C W-Complexes Chapter 7 Cobordism 1.Cobordism and Transversality 2.The Thorn Homomorphism Chapter 8 Isotopy 1.Extending Isotopies 2.Gluing Manifolds Together 3.Isotopies of Disks Chapter 9 Surfaces 1.Models of Surfaces 2.Characterization of the Disk 3.The Classification of Compact Surfaces Bibliooraphy Appendix Index