The performance of a process, such as aircraft fuel consumption, can be enhanced when its most effective controls and operating points are determined. Primer on Optimal Control Theory provides an introduction to the theory behind analysing these processes and finding the best controls, which provides a sound basis for those wishing to tackle more advanced literature. The book presents the important concepts of weak and strong control variations leading to local necessary conditions, and also global sufficiency of Hamilton–Jacobi–Bellman theory. It also gives the second variation for local optimality where the associated Riccati equation is derived from the transition matrix of the Hamiltonian system. These ideas lead naturally to the development of H2 and H∞ synthesis algorithms. This book will enable applied mathematicians, engineers, scientists, biomedical researchers, and economists to understand and implement optimal control theory at a level of sufficient generality and applicability for most practical purposes.