In this project, we are successfully discussed to contour integral and its applications.Contour integration is closely related to the calculus of residues. One of the advantage ofcontour integrals is the evaluation of integrals along the real line that are not readily foundby using only real variable methods. Contour integration methods include direct integrationof a complex – valued function along a curve in the complex plane, application of theCauchy integral formula and application of the residue theorem. The basic theorems and important prosperities on contour integration were discussed. Some applications of contourintegral both in mathematics and engineering have been considered with illustrativeexamples.