The spread of memes and misinformation on social media, political redistricting, gentrification in urban communities, pedestrian movement in crowds, and the dynamics of voters are among the many social phenomena that researchers investigate in the field of complex systems. In the study of complex social systems, there is also often societal relevance to improving our understanding of how individuals interact with each other and their environment, giving rise to collective group dynamics. The mathematical and computational study of complex social systems relies on and motivates the development of methods in many topics, including mathematical modeling, data analysis, network science, and topology and geometry. This volume is a collection of a variety of articles about complex social systems. This collection includes both (1) survey and tutorial articles that introduce complex social systems and methods to study them and (2) manuscripts with original research that highlight a variety of mathematical areas and applications. In short, this book introduces the study of complex social systems to a broad mathematical audience. It will be of particular interest to people who are interested in applied mathematics.