This is quite possibly the first book on practical methods that combines nonlinear optimization, mathematical control theory, and numerical solution of ordinary differential or differential-algebraic equations to successfully solve optimal control problems. The focus of the book is on practical methods, i.e., methods that the author has found to actually work. Everything described in the book has been implemented in production software and used to solve real problems. The author's general discussion of the topic maintains a focused and concise presentation. Using modern computational methods based on nonlinear programming algorithms, he introduces the basic material necessary to solve an optimal control problem. There are two major parts of a successful optimal control solution technique. The first part is the optimization method. The second part is the differential equation method. Betts's goal is to suggest that methods used to solve differential equations and optimize the functions are intimately related.