Abstract
In this paper, we initiate the study of generalized topological groups. A generalized topological group has the algebraic structure of groups and the topological structure of a generalized topological space defined by A. Csaszar [2] and they are joined together by the requirement that multiplication and inversion are G-continuous. Every topological group is a G-topological group whereas converse is not true in general. Quotients of generalized topological groups are defined and studied.