This in-depth, self-contained introduction to optical waveguide analysis, will be of great use to engineers and researchers in all fields using guided-wave optics--from fiber optics communication to integrated optical electronics. Part one examines various analytic approximation methods for three-layer optical dielectric waveguides, uniform core optical fiber, and 2-D and 3-D optical waveguides. Part two details the finite-element method--a numerical technique for cases in which approximation methods are inadequate. Numerous illustrative examples demonstrate the analysis of 2-D and 3-D optical waveguides, axisymmetric and non-axisymmetric optical fibers, and nonlinear optical waveguides.