This comprehensive introduction to political extremism goes far beyond a mere description of the different types of extremism. Instead, the authors provide a systematic approach to the topic and examine the essential questions. The presentation of the research landscape and current concepts, theories, and methods in extremism research in the first part serves as a toolbox for the reader. In the second part, various forms of extremism, such as right-wing and left-wing extremism as well as religious extremism, are classified and explained.