In this book, we systematically discussed the background, theory and methods, and selected applications of embodied multi-agent system. Specially, in Part I, we first reviewed the history of embodied intelligence and presented a general architecture about it. Then, we provided a general introduction to the more specific topic of embodied multi-agent system. Followed by them, we presented a series of methods to tackle the perception-action loop, embodied cooperation, and competitive learning. Finally, we presented some advanced applications including large language models, simulation platforms, and physical robotic validation.