The main objective of this thesis is to study and solve the Volterra integral and integro-differential equation and some scientific models for real life problems.This objective may be divided into three sub objectives, as follows: The first one is to classify and study the subject of the integral equations and to supply the basic definitions related to the Volterra integral and integro-differential equations. In the second sub objective we used the " dafterdar-jafari method " to solve Volterra integral and integro-differential equations. The third sub objective is to introduce another iterative method which is called the power series method to provide a solution of the Volterra integral and integro-differential equations. Finally, the application of the dafterdar-jafari method and the power series method are presented for finding the analytic and approximate solution for some real life scientific problems, namely, Volterra’s population model, the hybrid selection model, Riccati equation and the logistic model. Also, it is important to remark that the computer programs are coded using the computer software Mathematica.8.