Let G be a finite group of order ;Multipliers are of great importance in proving nonexistence or construction of difference sets. In Chapter II, we first prove a general multiplier theorem for central elements in a group ring. This multiplier theorem unifies and improves most previous multiplier theorems, it also gives new multipliers. Next we view the numerical multiplier group of an abelian difference set as Galois group of certain number field extension. From this we get an upper bound for the size of the multiplier groups of cyclic difference sets. Also by using this number theoretic approach, we prove that a prime p is a multiplier of D if and only if p splits completely in ;In Chapter III, we study skew Hadamard difference sets. The field ;In Chapter IV, we study reversible abelian difference sets. In this case ;Once McFarland's conjecture is proved, the study of reversible abelian difference sets is reduced to the case when
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