The chapter "Communities in Networks" by Mason A. Porter, Jukka-Pekka Onnela, and Peter J. Mucha explores the concept of communities within networks, which are groups of nodes that are densely connected to each other but sparsely connected to other dense groups. The authors discuss the historical development of the study of social communities and the mathematical tools used to analyze them, including spectral partitioning, modularity optimization, and spectral methods. They highlight the importance of community structure in understanding the dynamics of networks, such as the spread of opinions and diseases. The chapter also reviews various community detection algorithms, including traditional clustering techniques, hierarchical and divisive methods, centrality-based approaches, and local methods like $k$-clique percolation. The authors emphasize the need for multiple computational heuristics to balance the quality of identified communities with computational efficiency, and they discuss the challenges and limitations of current methods, particularly in handling dense networks and overlapping communities.The chapter "Communities in Networks" by Mason A. Porter, Jukka-Pekka Onnela, and Peter J. Mucha explores the concept of communities within networks, which are groups of nodes that are densely connected to each other but sparsely connected to other dense groups. The authors discuss the historical development of the study of social communities and the mathematical tools used to analyze them, including spectral partitioning, modularity optimization, and spectral methods. They highlight the importance of community structure in understanding the dynamics of networks, such as the spread of opinions and diseases. The chapter also reviews various community detection algorithms, including traditional clustering techniques, hierarchical and divisive methods, centrality-based approaches, and local methods like $k$-clique percolation. The authors emphasize the need for multiple computational heuristics to balance the quality of identified communities with computational efficiency, and they discuss the challenges and limitations of current methods, particularly in handling dense networks and overlapping communities.