"Electromagnetic field theory is a discipline concerned with the study of charges, at rest and in motion, that produce currents and electric-magnetic fields. It is, therefore, fundamental to the study of electrical engineering and physics and indispensable to the understanding, design, and operation of many practical systems using antennas, scattering, microwave circuits and devices, radio-frequency and optical communications, wireless communications, broadcasting, geosciences and remote sensing, radar, radio astronomy, quantum electronics, solid-state circuits and devices, electromechanical energy conversion, and even computers. Circuit theory, a required area in the study of electrical engineering, is a special case of electromagnetic theory, and it is valid when the physical dimensions of the circuit are small compared to the wavelength. Circuit concepts, which deal primarily with lumped elements, must be modified to include distributed elements and coupling phenomena in studies of advanced systems. For example, signal propagation, distortion, and coupling in microstrip lines used in the design of sophisticated systems (such as computers and electronic packages of integrated circuits) can be properly accounted for only by understanding the electromagnetic field interactions associated with them. The study of electromagnetics includes both theoretical and applied concepts. The theoretical concepts are described by a set of basic laws formulated primarily through experiments conducted during the nineteenth century by many scientists-Faraday, Ampere, Gauss, Lenz, Coulomb, Volta, and others. Although Maxwell had come up with 20 equations with 20 variables, it was Heaviside and Hertz that both independently put them into a consistent and compact vectorial form. Both Heaviside and Hertz named them in honor of Maxwell, and today they are the widely acclaimed Maxwell's equations. The applied concepts of electromagnetics are formulated by applying the theoretical concepts to the design and operation of practical systems. In this chapter, we will review Maxwell's equations (both in differential and integral forms), describe the relations between electromagnetic field and circuit theories, derive the boundary conditions associated with electric and magnetic field behavior across interfaces, relate power and energy concepts for electromagnetic field and circuit theories, and specialize all these equations, relations, conditions, concepts, and theories to the study of time-harmonic fields."-- Provided by publisher.