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This book offers a concise yet comprehensive exploration of embodied artificial intelligence (AI) and its integration with swarm manipulation, navigation, and tracking tasks. It uniquely bridges the gap in the existing literature by providing a thorough review of swarm-embodied AI, focusing on collaborative perception and decision-making methods. Its standout features include a systematic approach, detailed discussions on advanced directions, and a practical case study on multi-robot multi-target tracking. It commences by examining the three key elements of embodied AI: multi-sensor fusion, embodied perception, and embodied decision-making. It reviews existing works that independently optimize each of these elements. Subsequently, the book delves into swarm-embodied AI, encompassing swarm-embodied collaborative perception, collaborative decision-making, and future research directions. Specifically, it explores how swarm intelligence enhances the scalability and generalizability of embodied AI, and conversely, how embodied AI augments swarm intelligence by adapting learning models to diverse tasks and environments. Finally, the book presents a case study of multi-robot multi-target tracking, providing a practical demonstration of all algorithms discussed within. Readers can follow this case study step by step to gain a deeper understanding of the advancements and potential challenges of swarm-embodied AI. Designed with accessibility in mind, this book caters to a wide audience, including researchers, students, and practitioners seeking insights into this rapidly evolving field. Its user-friendly format ensures ease of understanding without requiring specialized prior knowledge. By distilling complex concepts and highlighting practical applications, the book serves as an invaluable resource for anyone interested in the intersection of embodied AI and swarm intelligence.