This book contains two parts: The first six chapters present the modern mathematical theory of boundary integral equations with applications on fundamental problems in continuum mechanics and electromagnetics, while the second six chapters present an introduction to the basic theory of classical pseudo-differential operators so that the particular boundary integral equations arising in the aforementioned applications can be recast as pseudo-differential equations which serve as concrete examples illustrating the basic ideas how one may apply the theory of pseudo-differential operators and their calculus to obtain basic properties for the corresponding boundary integral operators. The book is unique in the sense that no existing books provided these two complimentary features simultaneously The two new chapters on Maxwell’s equations summarizing the most up-to-date results in the literature. The book is unique in the sense that these two chapters are sufficiently enough to serve as an introduction to the modern mathematical theory of boundary integral equations in electromagnetics and provide the mathematical foundation of boundary element methods for computational electromagnetics This book is unique in the sense that it includes theory and applications of boundary integral equations arising in potential flow, acoustics, elasticity, Stokes flow and electromagnetics. Because of the breadth of these applications, it will attract a broader readership than any of the exiting books