Equations of Mathematical Diffraction Theory is a comprehensive treatment of comparative analysis and the development of efficient analytical methods for solving equations of mathematical diffraction theory. It considers some general properties of integral and differential operators in the context of the linear theory of diffraction processes, gives estimates of the operator norms for various ranges of the wave number variation, and studies the spectral properties of these operators. The author also presents a new analytical method for constructing asymptotic solutions of boundary integral equations in mathematical diffraction theory for the high-frequency case.