Scattering of waves from material objects and abstract potentials is a large part of modern mathematical physics with wide applications from geophysics and medical imaging to relatively recent near-field physics and technology making almost unrestricted imaging resolution possible. These have led to profound advancements in scattering and inverse scattering theories. Scattering of Waves: Applied Theory explores the underlying concepts, physics and mathematics of wave scattering and wave field structures and self-consistently introduces a range of topics in scalar acoustics and quantum and vector electromagnetic scattering. Features: A unified and comprehensive presentation of Laplace, Poisson, Helmholtz and wave equations, d'Alembert's solution, Poisson's spherical means, Hadamard's method of descent and the equations of Euler-Poisson-Darboux and Kirchoff, their revealing physical imports and connections with Huygen's principle. Also included are Maxwell's equations, gauges, energy and momentum conservations. A concise introduction to the concepts of domain differentiation, angular spectrum, principal volume and cavity definition used in the derivations. Extensive treatments of Green's functions and tensors, delta derivatives, transverse delta function, point approximation of electromagnetic Green's tensor, distributional calculations of the mixed derivatives of scalar Green's function and the depolarizing dyadic. An in-depth presentation of the integral method in scattering and the Huygen-Fresnel, Fresnel-Kirchoff and Helmholtz integral representations of the scattered fields. Also provided a comprehensive historical antecedents alongside modern quantitative development. Extensive discussions of time dependent and stationary formal scattering theory; resolvent, Green and wave operators, S and T matrices; detailed compilations of numerous operator relations and identities; scattering amplitude; its properties and Fourier transform relation with T-matrix. Detailed derivations of the optical theorem; field equivalence principles; physics and mathematics of evanescent waves and near-field implications of the derived expressions. Expressions are mostly derived explicitly and whenever possible, from more than a single perspective. Often, there arise controversies among experts on some derivations and interpretations. These are brought out whenever they appear for the reader to form his or her own opinion. Primarily aimed at advanced students of physics, engineering and applied mathematics, this text will also be valuable to researchers and faculties in electromagnetics, acoustics and quantum mechanics.