This book provides the fundamentals of dynamic optimization which can be used to improve the performance of engineering systems. Most results are derived using the theory of calculus of variations. The methods are illustrated by a number of examples. Numerical implementation of the theory by direct and indirect methods is also described. Computer programs are provided that can be used to work out engineering problems. The book also introduces some new results in dynamic optimization using higher-order approaches. The book is appropriate for undergraduate seniors or first-year graduate students. It should also be of interest to professionals in the areas of automotive, aerospace, or manufacturing engineering. Students and researchers in the areas of systems theory, control, and optimization will benefit from the relatively simple exposition in this book.