The concept of segal algebra is originated from Reiter work that is generalized by Burnham from -subalgebras to the arbitrary Banach algebras. A Banach algebra is a segal algebra in anach algebra if is a dense ideal in and for each and constunt , we have: . Also a egal algebra is a Banach algebra which is a dense ideal in algebra which is not necessarily self-aljoint. The main difference between algebras and segal algebra is that; segal algebras don’t have approximate identity necessarily. As there is no Gelfand-Naimark theorem for segal algebras, there is not enough information about the general structure of these type of algebras. In this thesis the theory of the commutative segal algebras with the emphasyis on their functional representations is extended. In fact the Gelfand-Naimark theorem is extended from algebras to a large type="#_x0000_t75" segal algebras.
