Linear and non-linear integral equations of the first and second kinds have many applications in engineering and real life problems. Thus, we try to find efficient and accurate methods to solve these problems. The aim of this editorial is to overview the content of the Special Issue "Integral Equations: Theories, Approximations and Applications". This Special Issue collects innovative contributions addressing the top challenges in integral equations, integro-differential equations, multi-dimensional problems, and ill-posed and singular problems with modern applications. It covers linear and non-linear integral equations of the first and second kinds, singular and ill-posed kernels, system of integral equations, high-dimensional problems, and especially new numerical, analytical, and semi-analytical methods for solving the problems mentioned by focusing on modern applications.

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