This course has two objectives. First, it provides a rigorous introduction to a standard set of topics in modern macroeconomic theory, such as economic growth, business cycle theory, consumption theory, monetary policy and fiscal policy. Second, the course develops the analytical tools required to study the above topics within a dynamic optimization framework. This is an advanced course aimed for students with a solid background in macroeconomic and microeconomic theory, linear algebra and calculus. It is particularly recommended for students interested in pursuing a graduate degree in economics.