Contour integration is a technique in complex analysis used to evaluate integrals along a specified path, or contour, in the complex plane. This method is particularly useful for integrating functions that are difficult to handle using traditional real analysis techniques. By applying the residue theorem, one can compute integrals by considering the singularities of the function within the contour. The process involves selecting a contour that encloses the singularities and then calculating the integral based on the residues at those points. Contour integration is widely applied in various fields, including physics and engineering, particularly in problems involving Laplace transforms and Fourier transforms.