safia mahgoub alsadaig2017-08-092017-08-092015http://hdl.handle.net/123456789/4708A BSTRACT This thesis treats functional analysis and its application. We study function spaces with analytical structures, such as normed spaces, banach spaces and Hilbert spaces. Our prime interest is in the most fundamental theorems of functional analysis. There is Hanh-banach theorem, uniform boundedness theorem, and closed graph theorem. We give applications to Fourier analysis and applications on existence of solution of differential and integration equations.الرياضياتMathematical Statistics