This introduction presents an overview of the key concepts discussed in the subsequent chapters of this book. The book examines the vector finite-element approach and describes details of such vector field constraints for anisotropic media. It introduces an effective acceleration technique to speed up the nonlinear iteration process. The book discusses to reduce errors and the time involved in data preparation, an automatic mesh generation algorithm for triangular elements. It also discusses in selecting solution techniques for the algebraic matrix equation, the nature of the problem is scrutinised and several efficient solution methods. The book argues that the effective modal index is extracted as the eigenvalue for given guided power. Linear and nonlinear coupled optical waveguides are most useful devices in optical signal processing. Linear and nonlinear coupled-mode equations, applicable to vector-mode coupling in anisotropic and lossy media, are derived by using a reciprocity approach.