Formal methods originate from theoretical computer science and have become a vibrant and interdisciplinary field. At its core, formal methods include formulating specifications to form proof obligations, verifying that the systems indeed meet their specifications via algorithmic proof search, and designing systems to meet those obligations. This course introduces fundamental theories and techniques of formal methods that apply broadly to various dynamical systems, such as robots, autonomous systems and cyber physical systems. Particularly, the following major topics will be covered: formal modeling of systems, formal properties such as regular and omega-regular properties, simulation and abstraction, linear temporal logic (LTL), automata based model checking and game theoretic formal control synthesis and real world engineering applications.