This book examines the concept of stigmatism from its base to the most fundamental stigmatic systems. The book begins with Maxwell's equations, before continuing with the wave equation, the eikonal equation and the ray equation. The eikonal equation is also studied with the formalism of the calculation of variations and the concept of stigmatism. Once the foundations of stigmatism have been established, the book focuses on fundamental stigmatic systems, Cartesian ovals and stigmatic lenses. Step by step, the derivations of these systems are obtained and illustrative examples of all their cases are shown. Through the study of these systems, the uniqueness of stigmatism is formulated, and the implications of this uniqueness are presented at the end of the book. This book is an excellent guide for producers of lenses and optical products, and academics in lens design and optics.