This article is an introduction to complexity theory, which will be discussed using the example of economic science. In this context, a short historical overview is intended to demonstrate why the traditional mechanistic worldview persistently remains a part of economic science and how it led to the development of the theory of complex systems, which, for example, can be subsumed under chaos theory. Furthermore, a simple supply and demand model is employed as an example to discuss this new theory and to describe the characteristics of complexity in comparison with the general mechanistic principle. For this purpose, specially designed software is used for the simulation and analysis of selected complex systems.