Integral equations are a mathematical tool to model a variety of problems, ranging from physics to engineering, from finance to medicine, just to cite a few. Even if several approximation techniques have been introduced in the literature, the research in this field is still going on, both from theoretical and applicative point of view. The mini-symposium aims at presenting new results in the field of numerical methods for such type of equations, with emphasis on theoretical developments, computational efficiency, and real-world applications. Additionally, it seeks to foster interdisciplinary collaboration and inspire new research directions in the area.