In this thesis , we present an expanded account of the work done by Hawa Alsanousi Hamouda . First we will introduce essential definitions and basic information which will be used in this thesis. Let G always denote a locally compact group with a Haar measure and modular function . Let be the Banach space of measurable functions such that and when we letdenote the Dirac measure at s . In addition , we let denote the set of all continuous function vanishing at and denote the set of all complex regular Borel measures on $ G In Chapter 2 , we will give basic information about algebras , and we develop an amenability theory in the very general context of a group action on the predual of a von Neumann algebra . In fact , will give proofs of Stokke's statements in section one of his paper [21] and some Finally , the last chapter deals with the generalization of Lau and Ghaffari’s results in their papers respectively other statements that are not contained in his paper .