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Most real-world systems are to some degree nonlinear, and the addition of nonlinearity can lead to qualitatively different kinds of behavior as compared with linear systems. This course provides an introduction to the analysis of nonlinear dynamical systems, with examples drawn from across the sciences and engineering. In addition to formal analysis, the course will emphasize qualitative and geometric thinking. Topics will include one-dimensional systems; bifurcations; phase-plane analysis; nonlinear oscillators; and chaos, fractals, and strange attractors. Prerequisites: Differential equations at the level of CME 102 and linear algebra at the level of CME 104; some programming experience.