|1. Introduction. 2. Mathematical preliminaries for optimal control. 3. Classical linear quadratic optimal control, including regulation & tracking control. 4. Observer based optimal control (LQG control). 5. Loop shaping and LTR control. This is a course designed for graduate students which will provide techniques that can help you to design an optimal controller for linear systems with a specific performance index. Concepts such as optimality condition, linear quadratic regulation (LQR), and linear quadratic gaussian (LQG) problem are introduced in the course. In addition, the course also includes the loop shaping concept and the loop transfer recovery (LTR) technique which are frequently used in the modern control.