The chapter "Networks beyond pairwise interactions: structure and dynamics" by Federico Battiston, Giulia Cencetti, Iacopo Iacopini, Vito Latora, Maxime Lucas, Alice Patania, Jean-Gabriel Young, and Giovanni Petri provides an overview of the emerging field of networks that go beyond pairwise interactions. The complexity of many biological, social, and technological systems stems from the richness of interactions among their units. While traditional network models have been successful in describing systems with pairwise interactions, recent research has shown that higher-order interactions, such as groups of three or more nodes, are crucial for understanding and predicting the dynamics of these systems. The chapter begins by discussing methods to represent higher-order interactions, including graph-based representations, explicit higher-order representations, and bipartite graph representations. It highlights the limitations of traditional graph representations in capturing group interactions and introduces more sophisticated frameworks like simplicial complexes and hypergraphs. These frameworks allow for a more detailed and accurate description of higher-order interactions. The chapter then reviews measures designed to characterize the structure of higher-order systems, such as incidence and adjacency matrices, walks, paths, and centrality measures. It also discusses models for generating synthetic higher-order structures, including random and growing simplicial complexes, bipartite graphs, and hypergraphs. The dynamics of higher-order systems are explored in the following sections, focusing on diffusion, synchronization, spreading, and social dynamics. The chapter highlights novel emergent phenomena that arise when processes are extended beyond pairwise interactions, such as higher-order diffusion, random walks on simplicial complexes, and synchronization in complex networks. Finally, the chapter provides an overview of real-world applications of higher-order networks, including social systems, neuroscience, ecology, and other biological systems. It concludes with a discussion of current modeling and conceptual frontiers in the field, emphasizing the importance of higher-order interactions in understanding complex systems.The chapter "Networks beyond pairwise interactions: structure and dynamics" by Federico Battiston, Giulia Cencetti, Iacopo Iacopini, Vito Latora, Maxime Lucas, Alice Patania, Jean-Gabriel Young, and Giovanni Petri provides an overview of the emerging field of networks that go beyond pairwise interactions. The complexity of many biological, social, and technological systems stems from the richness of interactions among their units. While traditional network models have been successful in describing systems with pairwise interactions, recent research has shown that higher-order interactions, such as groups of three or more nodes, are crucial for understanding and predicting the dynamics of these systems. The chapter begins by discussing methods to represent higher-order interactions, including graph-based representations, explicit higher-order representations, and bipartite graph representations. It highlights the limitations of traditional graph representations in capturing group interactions and introduces more sophisticated frameworks like simplicial complexes and hypergraphs. These frameworks allow for a more detailed and accurate description of higher-order interactions. The chapter then reviews measures designed to characterize the structure of higher-order systems, such as incidence and adjacency matrices, walks, paths, and centrality measures. It also discusses models for generating synthetic higher-order structures, including random and growing simplicial complexes, bipartite graphs, and hypergraphs. The dynamics of higher-order systems are explored in the following sections, focusing on diffusion, synchronization, spreading, and social dynamics. The chapter highlights novel emergent phenomena that arise when processes are extended beyond pairwise interactions, such as higher-order diffusion, random walks on simplicial complexes, and synchronization in complex networks. Finally, the chapter provides an overview of real-world applications of higher-order networks, including social systems, neuroscience, ecology, and other biological systems. It concludes with a discussion of current modeling and conceptual frontiers in the field, emphasizing the importance of higher-order interactions in understanding complex systems.