Business Cycle research strives to analyze and explain short-run fluctuations in key macroeconomic variables such as production output, income, employment, and prices. The course develops mathematical models which unveil the structural reasons for these fluctuations and the underlying economic mechanisms. Starting with the class of so-called Real Business Cycle (RBC) models, particular emphasis is placed on models of the labor market including models with labor indivisibilities, search-and matching, and home production. Based on the findings obtained, policy implications and the general scope for fiscal and monetary policy to stabilize the economy and foster production output, employment, and price stability are investigated. Numerical simulations based on realistic (calibrated) parameter choices are employed to replicate the empirically observed patterns and to quantify the effects of different policies. Participants of the course are provided with MATLAB scripts allowing them to replicate the simulation results presented in class.