Propagation of electromagnetic waves inside a GRIN medium is studied in this chapter. Section 2.1 starts with Maxwell’s equations and uses them to derive a wave equation in the frequency domain. A mode based technique is used in Section 2.2 for solving the wave equation for a GRIN device fabricated with a parabolic index profile. The properties of both the Hermite’Gauss and the Laguerre-Gauss modes are discussed. Section 2.3 is devoted to other power-law index profiles and employs the Wentzel-Kramers Brillouin method to discuss the properties of modes supported by them. We discuss in Section 2.4 the relative efficiency with which different modes are excited by an optical beam incident on a GRIN medium. The intermodal dispersive effects that become important for pulsed beams are also covered. Section 2.5 describes several non-modal techniques that can be used for studying wave propagation in GRIN media.