1 Differentiable Manifolds and Vector Fields -- ยง0 Calculus in ?n and Differentiable Manifolds -- ยง1 Vector Fields on Manifolds -- ยง2 The Topology of the Space of Cr Maps -- ยง3 Transversality -- ยง4 Structural Stability -- 2 Local Stability -- ยง1 The Tubular Flow Theorem -- ยง2 Linear Vector Fields -- ยง3 Singularities and Hyperbolic Fixed Points -- ยง4 Local Stability -- ยง5 Local Classification -- ยง6 Invariant Manifolds -- ยง7 The ?-lemma (Inclination Lemma). Geometrical Proof of Local Stability -- 3 The Kupka-Smale Theorem -- ยง1 The Poincarรฉ Map -- ยง2 Genericity of Vector Fields Whose Closed Orbits Are Hyperbolic -- ยง3 Transversality of the Invariant Manifolds -- 4 Genericity and Stability of Morse-Smale Vector Fields -- ยง1 Morse-Smale Vector Fields; Structural Stability -- ยง2 Density of Morse-Smale Vector Fields on Orientable Surfaces -- ยง3 Generalizations -- ยง4 General Comments on Structural Stability. Other Topics -- References