English : We commence by using from a new norm on L 1 (G) the *-algebra of all integral functions on locally compact group G, to make the C * algebra C * (G). Consequently, we find its dual B(G), which is a Banach algebra so-called Fourier-Stieltjes algebra, in the set of all continuous functions on G. We study Banach algebra A(G), Fourier Algebra, and approach to its dual; Accordingly, we find Von Neumann algebra VN(G), the dual of A(G) and consider lots of its important properties. Studying Fourier algebra for locally compact Abelian group G, we consider the identify relation between Fourier algebra and Fourier transformation for locally compact Abelian groups. Eventually, by defining Segal algebras and Segal algebras, we establish Lebesgue-Fourier algebra SA(G). Its dramatic property as a Segal algebra and even an Segal algebra for A(G), is followed in some theorems.