This chapter introduces the basic concepts of Model Predictive Control (MPC) theory necessary to design the controller in later chapters. With a focus on MPC for linear systems, the design of controllers with different objective functions is covered, and some key methods such as reference tracking are presented while elaborating on implementation details. Experiments with a toy problem are included, showing the effect of tuning the different controller parameters, and adding different control and state constraints, both linear and nonlinear.