This course provides an excellent example of the application of abstract mathematics. The study of the time evolution of mathematical models of real-world phenomena from economics, computer science, biology, ecology, engineering, finance, physics, etc., applies methods and techniques from geometry, topology, differential and difference equations, measure theory, etc. Moreover, the use of computer algebra systems such as MatLab allows for the detailed development of non-trivial models of concrete dynamical systems. This course is an introduction to discrete and continuous dynamical systems. The goal is to provide a set of tools that can be used to understand such systems from a qualitative and quantitative perspective. Possible topics will include linear and nonlinear phase portraits, limit sets (fixed points, orbits, etc.), stability, bifurcations, chaos, fractals, etc. Concepts and methods from geometry, topology, and analysis will be introduced along the way.