This course is designed for graduate students in Mathematics. Students have taken a first course in P.D.E's can register for the course and get benefit of its topics. In this course, we discuss in details Integral Equations and other related topics, such as, Laplace transform and calculus of variations. Integral Equations come from real life physical problems and beside that D.E's and P.D.E?s can be transformed into Integral and integro- differential equations