Introduction

This chapter serves two purposes. First, it provides a history of how the concept of coherent states was germinated and who made some of the most fundamental theoretical developments in the twentieth century. Second, it outlines the most important outcome of these developments was how the underlying mathematical structure of coherent states is a branch of mathematics known as Lie groups and Lie algebras. Utilizing the coherent state concept, and leveraging the mathematical structures usability, a plethora of physical applications, such as quantum phase transitions and quantum chaos, is discussed in later chapters.