الفهرس 
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Abstract
The main purpose of this thesis to present and use the Adomains decomposition method (ADM) and the numerical quadrature techniques in solving linear and nonlinear untegral equations and systems of such equations. ADM was developed by Adomain at the beginning of 1980 . It has been applied to solve many linear and nonlinear functional equations. It is a powerful, very effective and reliable device for solving deterministic and stochastic equations as well as systems of such equations. Quadrature methods is a very important and powerful numerical method for evaluating an approximation to definite integrals and hence for solving integral equations. In this work, ADMis applied to solve a class of integral equations . Some converence theorems were discussed. It is used to solve some different problems and systems of such problems which illustrate the reliability of the method. To ensre that the ADM is very powerful tool in solving nonlinear problems, we compare it with a numerical technique which is the quadrature methods. It is found that the ADM requires less computational efforts to obtain an accurate approximate solution..