Residue theory is a concept in complex analysis, a branch of mathematics that studies functions of complex numbers. It focuses on calculating integrals of complex functions around singular points, which are points where the function is not defined or behaves irregularly. The residue of a function at a singularity provides valuable information about the behavior of the function near that point. The main tool of residue theory is the Residue Theorem, which states that the integral of a function around a closed contour can be determined by the sum of residues at the singularities inside that contour. This theorem simplifies the process of evaluating complex integrals, making it a powerful technique in both mathematics and physics.