Recent advances in the field of guided-wave optics, such as fibre optics and integrated optics, have included the introduction of various optical waveguides. Computational tools for modelling and simulation are essential for a successful design, optimization, and realization of the optical waveguides. Despite its relatively brief existence, the finite element method has grown into a powerful and efficient tool for solving the most general optical waveguide problems. In this book, starting with a brief review of electromagnetic theory for optical waveguide analysis, the concepts of the finite element method and its fundamentals are discussed in detail. Current topics of the application of the finite element method to various optical waveguide problems, such as planar optical waveguides, optical channel waveguides, optical fibres, polarization-maintaining optical fibres, optical gratings, optical waveguide discontinuities, nonlinear optical waveguides, optical solitons and quantum well structures, are described, including many illustrations.