Abstract: We will provide a concise introduction to the problem of optimally controlling a linear system driven by white, Gaussian nose, and where the cost function is quadratic. We will comment on similarities and differences with the discrete state and action space MDPs, which are the most common model in the reinforcement literature. Unlike general MDPs, LQG problems with both full information and partial information admit closed-form optimal solutions. The tutorial will present a derivation of these results.