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This book is an extensive revision of the 2007 book Random Graph Dynamics. In contrast to the first edition, the new version considers a small number of types of graphs, primarily the configuration model and inhomogeneous random graphs, but investigates a wide variety of dynamics. It describes results on convergence to equilibrium for random walks on random graphs as well as topics that have emerged as mature research areas since the publication of the first edition, such as epidemics, the contact process, voter models, and coalescing random walk. Furthermore, Chapter 8 discusses a new, challenging, and largely uncharted direction: systems in which the graph and the states of their vertices coevolve.