Introduction

We begin by reviewing typical liquid crystal and mathematical optics problems, which are seemingly disjoint. We then provide a brief history of such optics problems, especially related to nonlinear partial differential equations of Monge–Ampère type. One of the central themes of this book is also introduced: Snell’s Law. After some initial discussion on the challenges of bringing the seemingly distinct research areas together, we provide motivation for doing so, namely, understanding optical phenomena in liquid crystals. Finally, a brief summary of each forthcoming chapter is provided. Topics to be addressed in later chapters range from variational methods related to Fermat’s principle in anisotropic, inhomogeneous media to optical phenomena in chiral media (in particular, cholesteric liquid crystals).