Cyber-physical systems with underlying interconnected network structures can today be found in various domains such as robotic, sensor, social, and power networks. In this lecture, we provide a mathematical introduction to the framework of multi-agent dynamical systems and study various fundamental phenomena arising in such systems. We will cover important topics related to the analysis of multi-agent networks via algebraic graph theory and their application to engineering problems such as consensus in averaging systems, stable equilibria in compartmental flow networks, and synchronization in networked systems and coupled oscillators.