The aim of this course is to give an understanding of fundamental concepts used to describe complex systems. As examples, chaotic low-dimensional systems, self-organizing systems, and cellular automata are discussed. The fact that systems composed of a large number of simple components can exhibit complex phenomena is exemplified in, for example, self-organising systems (in the form of chemical reaction-diffusion systems), the second law of thermodynamics (as a statistical result of large physical systems), neural networks, evolution of cooperation, cellular automata (as an example of an abstract computational class of systems), economic systems of interacting trading agents, urban growth and traffic systems. There is no universal definition of a complex system, but there are several features that are usually brought up when a system is considered complex, typically involving order/disorder and correlations. An important scientific question is whether these and other characteristics of the systems can be quantified in a comprehensive…