Accessible, concise, and self-contained, this book offers an outstanding introduction to three related subjects: differential geometry, differential topology, and dynamical systems. Topics of special interest addressed in the book include Brouwer's fixed point theorem, Morse Theory, and the geodesic flow. Smooth manifolds, Riemannian metrics

Manifolds. Vector Fields and Dynamical Systems. Riemannian Metrics. Riemannian Connections and Geodesics. Curvature. Tensors and Differential Forms. Fixed Points and Intersection Numbers. Morse Theory. Hyperbolic Systems. References. Index.