The main theme of this thesis can be classified into five objects. These are summarized as follow: The first objective is to study the orthogonal functions, especially Walsh functions with its properties. The second objective is the using Walsh functions to modify an approach namely the Galerkin's method to solve any linear problems, especially the differential equations, integral equations, integro-differential equations and the eigenvalue problems. The third objective is to devote the last approach to solve any nonlinear problems especially the nonlinear differential equations. The fourth objective is to use these functions as a basis to solve some especial types of variational problems and given the generalization of it. The fifth objective is to give some real life applications for Walsh functions.