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The theory of integral equations has a close contact with many different areas of mathematics. This is sufficient to say that there is almost no area of applied sciences and physics where integral equations do not play an important role. This books intended primarily to study the existence of solution , analytically and numerically, of nonlinear integral equations of the second kind of types Hammerstein, Hammerstein- Volterra and Volterra-Hammerstein. Also, it is used for proving the existence and uniqueness solution, analytically, of linear integro-differential and integral equations of type Fredholm-Volterra in three dimensional. Finally, it is very useful in establishing the existence and uniqueness solution of linear and nonlinear partial differential equations of fractional order, analytically and numerically.