This book presents an overview of the theory of Integro-Differential Equations (InDEs). Beginning with the history of the inception of InDEs, the existence and uniqueness results for the initial value problem of InDEs is given. Next, stability concepts are discussed, including Lyapunov stability and Ulam-Rassias stability. Numerical techniques and operational matrix methods are also introduced. A specific study of second order InDEs of Fredholm InDes in complex plane is presented and an application to Finance is given.