This book explores the major techniques involved in optimization, control theory, and calculus of variations. The book serves as a concise contemporary guide to optimal control theory, optimization, numerical methods and beyond. As such, it is a valuable source to learn mathematical modeling and the mathematical nature of optimization and optimal control. The presence of a variety of exercises solved down to numerical values is one of the main characteristic features of the book. Another one is its compactness, and the material's usefulness in preparing and teaching several different university courses. The investigation of trends and their formation undertaken in the book leads seamlessly into extrapolation techniques and rigorous methods of scientific prediction. The research for this book was accomplished at the Russian Technological University (RTU) MIREA, based on the courses which have been taught at the RTU for many years.