The fundamental principle of model predictive control (MPC) is the solution of an optimization problem in real time. The optimization problem is designed in such a way that it reflects the goals of the control algorithm. For the development of MPC controllers for complex engine tasks, a solid knowledge of optimization is required. This chapter provides a brief overview of the fundamentals of optimization. Rather than an overview of the entire field, the optimization fundamentals are described that are particularly needed for the application of MPC in the field of combustion engines. The reader also is familiarized with the notation used. The chapter is to discuss various classifications of optimization problems. Furthermore, the concept of convexity is introduced. Additionally, the optimality conditions for nonlinear programs (NLP) are examined.