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

chapter 1|70 pages


chapter 2|38 pages

Vector Fields and Dynamical Systems

chapter 3|18 pages

Riemannian Metrics

chapter 4|44 pages

Riemannian Connections and Geodesics

chapter 5|54 pages


chapter 6|54 pages

Tensors and Differential Forms

chapter 7|48 pages

Fixed Points and Intersection Numbers

chapter 8|30 pages

Morse Theory

chapter 9|22 pages

Hyperbolic Systems