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0.1 Introduction The present volume is about the physics of electromagnetic scattering, not mathematics, and is intended as a reference book for engineering and physics students as well as researchers in electromagnetic scattering. Although the subject is on electromagnetic scattering, acoustic or scalar scattering will be discussed occasionally when it is deemed helpful and advantageous. In the current decade we are witnessing an emergence of inverse scattering theory. Before we embark on this exciting journey, perhaps this is an appropriate time to summarize and assess in one volume some of the important re? sults of electromagnetic scattering which have been found in recent decades. Since the end of WW II two significant physical phenomena in electromag? netic scattering, optimal polarization and exterior resonant frequencies, have been discovered and a powerful mathematical technique, called the integral equation method, has been incorporated. These physical quantities, which characterize the scattered field for a given scatterer, are not directly observ? able but can only be extracted by mathematical means from the measured scattering data. They are given special attention.1 Integral Representations for Fields.- 1.1 Preamble.- 1.2 Dyadic Calculus.- 1.3 The Free-space Dyadic Greens Function in R3.- 1.4 The Franz Representation for an Interior Problem in R3.- 1.5 The Franz Representations for Scattered Fields in R3.- 1.6 The Stratton-Chu Representation in R3.- 1.7 The Helmholtz Representation for Acoustic Fields.- 1.8 Volume Scattering: The Born Approximation.- 1.9 Rellichs Uniqueness Theorem.- 2 Polarization.- 2.1 Preliminary.- 2.2 Representation of Polarization.- 2.3 Stokes Vector for a Monochromatic Electric Field.- 2.4 Change of Polarization Basis.- 2.5 Superposition of Circularly Polarized Waves.- 2.6 Coherency Matrix for Quasi-Monochromatic Waves.- 2.7 Degree of Polarization.- 2.8 Decomposition of Partially Polarized Waves.- 3 Scattering Matrix.- 3.1 Scatlc(