Abstract
<p>This treatise is concerned with generalizations of the Multiplier Theorem for cyclic difference sets. These generalizations are presented in historical order.The Multiplier Theorem was initially established by M. Hall Jr., in 1947, for finite cyclic projective planes ((lamda) = 1). It was later extended, in 1951, by M. Hall Jr. and H. J. Ryser to the case where (lamda) > 1.Generalization of difference sets have led to the different generalizations of the multiplier theorem. The latest of these generalization was made in July, 1983.</p>