Optical Path Theory: Fundamentals to Freeform Adaptive Optics focuses on the potential to find analytical close form solutions using optical path theory to solve and design adaptive optics systems. With a thorough introduction to the subject, the first chapters of the book explore the three main axioms implemented in optical path theory: The Fermat Principle, Snell’s law, and the Malus-Duplin theorem. After the main axioms are presented, the book moves into exploring optical systems in the plane. The refractive mirror, refractive surface, lens, and the transfer function lens are discussed. Step-by-step equations are provided with each of these various systems to plot their waves, putting emphasis on the mathematical derivations and showing a variety of examples. As the various systems continue to be explored, they are generalized to three dimensions. Presented step-by-step mathematically, the generalization to three dimensions focuses on the key steps on each derivation. Theses generalizations are richer and lead to freeform shapes which are explored in detail. Mathematica codes for all the examples in the book are provided. With a step-by-step mathematical presentation of concepts, this book is complete with details, problems, solutions, and a multitude of useful examples.