What is a complex system? Although "complexity science" is used to understand phenomena as diverse as the behavior of honeybees, economic markets, the human brain, and the climate, there is no agreement about its foundations. In this introduction for students, academics, and general readers, philosopher of science James Ladyman and physicist Karoline Wiesner develop an account of complexity that brings the different concepts and mathematical measures applied to complex systems into a single framework. They introduce the different features of complex systems, discuss different conceptions of complexity in the literature, and develop their own account. They explain why complexity science is so important in today's world.