"Mathematical Modeling in Diffraction Theory Based on A Priori Information on the Analytical Properties of the Solution" provides the fundamental physical concepts behind the theory of wave diffraction and scattered wave fields as well as its application in radio physics, acoustics, optics, radio astronomy, biophysics, geophysics, and astrophysics. This book provides a coherent discussion of several advanced topics, which has the potential to push forward the progress in this field. The book begins with examples illustrating the importance of taking a priori information into account when developing algorithms for solving diffraction problems. The subsequent chapters discuss the basic analytical representations of wave fields; the auxiliary current and source methods for solving the problems of diffraction at compact scatterers; the null field and "T"-matrix methods widely used to solve problems in radio-physics, radio-astronomy, and biophysics; the continued boundary condition method, and the pattern equation method.