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Communities serve as basic structural building blocks for understanding the organization of many real-world networks, including social, biological, collaboration, and communication networks. Recently, community search over graphs has attracted significantly increasing attention, from small, simple, and static graphs to big, evolving, attributed, and location-based graphs. In this book, we first review the basic concepts of networks, communities, and various kinds of dense subgraph models. We then survey the state of the art in community search techniques on various kinds of networks across different application areas. Specifically, we discuss cohesive community search, attributed community search, social circle discovery, and geo-social group search. We highlight the challenges posed by different community search problems. We present their motivations, principles, methodologies, algorithms, and applications, and provide a comprehensive comparison of the existing techniques. This book finally concludes by listing publicly available real-world datasets and useful tools for facilitating further research, and by offering further readings and future directions of research in this important and growing area.