In this thesis, we present an expanded account of the work “Conditions implying the uniqueness of the weak*-topology on certain group algebras” done by Daws, Pham, and White. A dual Banach algebra is a Banach algebra which is a dual Banach space such that the product on is separately weak*-continuous. A dir=rtl align=right The main objective of this thesis is to examine naturally occurring Group measure algebras, M(G) for a locally compact group G, which are canonically dual spaces and find conditions which imply that the canonical predual (G) is unique. In fact, we give natural conditions on this important type="#_x0000_t75" (G) and M(G) which makes a certai natural comuliplication weak*-continuous). On going, we turn our attention to multipliers. We provide a simple criterion for showing that the multiplier algebra of a Banach algebra is actually a dual Banach algebra and show that dual Banach algebras always have multiplier algebras which are dual. Our result shows that M( (G))=M(G) are dual Banach algebras.