Contour integration is a method in complex analysis used to evaluate integrals along a specified path, or contour, in the complex plane. This technique is particularly useful for integrating functions that are difficult to handle using traditional real analysis methods. By applying the residue theorem, one can simplify the evaluation of integrals by focusing on the singularities of the function within the contour. The process involves defining a closed curve and calculating the integral of a complex function over that curve. Contour integration is essential in various fields, including physics and engineering, where it helps solve problems related to electromagnetism and fluid dynamics.