This chapter provides an introduction to the subject known as gradient-index optics. In Section 1.1, we present a historical perspective on this subject before introducing the essential concepts needed in later chapters. Section 1.2 is devoted to various types of refractive-index profiles employed for making gradient index devices, with particular emphasis to the parabolic index profile because of its practical importance. In Section 1.3, we discuss the relevant properties of such devices such as optical losses, chromatic dispersion, and intensity dependence of the refractive index occurring at high power levels. The focus of Section 1.4 is on the materials and the techniques used for fabricating gradient-index devices in the form of a rod or a thin fiber