The Residue Theorem is a powerful tool in complex analysis, a branch of mathematics that studies functions of complex numbers. It allows us to evaluate certain types of integrals by relating them to the residues of singularities within a closed contour. A residue is essentially the coefficient of the \frac1z term in the Laurent series expansion of a function around a singularity. Using the Residue Theorem, one can compute integrals over closed paths by summing the residues of the function's singularities inside the contour. This method simplifies calculations that would otherwise be complex and tedious, making it a fundamental technique in fields such as physics and engineering, where complex functions frequently arise.