This volume contains almost complete proceedings of the NATO Advanced Study Institute (ASI) organised in 1979 to bring together principal innovators and numerous users of mathematical techniques for analysing the interaction of electromagnetic waves with engineering and biological structures. The mathematical disciplines which can be brought to bear on these problems necessitate examination of effectiveness, convergence and robustness of the derived analytic and num~rical algorithms. The aim of this ASI was to give a clear and up-to-date tutorial presentation of available techniques, and to bring together interested scientists, engineers and mathematiciaris, to discuss together their experience and to ensure wider familiarity with the subject. Our programme consists of three distinct yet related parts. The first two of these reflect two somewhat different methods applicable for different ranges of L/A, where L represents a characteristic dimension of a structure and A is a representative wavelength-of radiation. The third part deals with the specific problem of biological interaction. In the first part (Low and Intermediate Frequency Applications) we offer tutorial texts and user-oriented discussions on main techniques and problems concerning: radiation, scattering, aperture penetration, inverse scattering, using moment methods and their developments. The approach to the high frequency applications forms the subject of the second part of this volume, concentrating mainly on the geometrical theory of diffraction (GTD). There are three main variants of the GTD: uniform theory of diffraction (UTD), uniform asymptotic theory (liAT) , spectral theory of diffraction (STD).