Volume XXXIX presents five review articles dealing with topics of current research interest in optics. The book opens with a chapter dealing with the analytic extension of the concept of geometrical optics rays into the complex domain. The extension is intimately related to inhomogeneous (evanescent) waves, which are currently of particular interest in connection with the rapidly developing area of near-field optics. The results are also relevant to investigations of wave attenuation in absorbing media, and to the understanding of light penetration into geometrical shadow regions, excitation of surface waves and propagation of Gaussian beams. In this article the principles are presented, with special emphasis on the physical significance of complex rays and their applications.