This course aims to provide an introduction to dynamical systems and their use in applied science. The theoretical introduction is illustrated by examples from technical applications and natural sciences. The module would be of interest to student in mathematics, especially but not exclusively applied mathematics, physics, engineering, or the natural and numerical sciences more broadly. It is a high level module hoping to draw interest from senior and exceptional junior students, especially those who wish to continue in one of the mentioned fields at university. As such, the module would be an excellent opportunity for such students to deepen their understanding in a more specific area of applied mathematics, having already familiarised themselves with the foundations. The focus of the module can be adjusted to cover more accessible examples based on the audience.