A course on topics in nonlinear physics. Finite dimensional flows, bifurcations, instabilities, and relation to phase transitions. Index theory and its use for the classification of topological defects. Chaos, strange attractors, maps, and fractals. To illustrate the nonlinear phenomena studied, we will draw examples from a diverse range of disciplines, including classical and quantum physics, but also chemistry, biology, and social sciences, to list only a few. Numerical exercises will be used throughout the course.