### Abstract:

Abstract
The reader may be surprised about what the linear integral equations. And that for the little importance that had paid for this topic.
The integral equations is a mathematics method which had used to solve many problems in physics and chemistry, and also at mathematic. Our considerable mathematic method can be also used to solve the differential equations which can be also reduces to a one of the integral equation.
Our research will consider the following points:-
1\ the definition of the linear integral equations, and explain some of its usefulness.
2\ some method of solution for the linear integral equations.
So in our first section we had to define the linear integral equations and we obtained some of its uses in mathematics, physics and chemistry, also we take the numerical solution for the linear integral equations. But we had just explained the method of solution for some reason we had written.
In the second section we explained a method to solve the integral equations of the first kind , and also it uses to solve the integral equations of the second kind .
At the third section we had the approximation solution, and we clear the co-theory for this method of solution.
More over our fourth section is specialized on the algebraically solution to the linear integral equations with the assistance theorems for it. And at special case for the kernel of the linear integral equations we take our fifth section and we joined our algebraically solution with Fourier series.
The sixth section had taken as applications to some problems which had reduced to an integral equation.
At last we had a conclusion to our research, and we take some problems in the last section as applications for the methods of solutions which we had explained in the previous sections.