Multi-Agent Systems (MAS) use networked multiple autonomous agents to accomplish complex tasks in areas such as space-based applications, smart grids, and machine learning. The overall system goal is achieved using local interactions among the agents. The last two decades have witnessed rapid development of MASs in automatic control. Tracing the roots of such systems back more than 50 years, this monograph provides the reader with an in-depth and comprehensive survey of the research in Multi-Agent Systems. The focus is on the research conducted in the two decades. It introduces the basic concepts and definitions to the reader before going on to describe how MAS has been used in most forms of systems. The monograph offers a concise reference for understanding the use of MASs and the contemporary research issues for further investigation. In addition to covering the basic theory, the authors also cover applications in multi-robot systems, sensor networks, smart grid, machine learning, social networks, and many-core microprocessors. On the Control of Multi-Agent Systems provides researchers and students in systems and control a modern, comprehensive survey of one of the most important current day topics.