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In Noetherian rings there is a hierarchy among regular, Gorenstein and Cohen-Macaulay rings. Regular non-Noetherian rings were originally deﬁned by Bertin in 1971. In 2007, Hamilton and Marley used Cech cohomology to introduce a theory of Cohen-Macaulay for non-Noetherian rings, answering a question posed by Glaz. This dissertation provides a theory of non-Noetherian Gorenstein rings agreeing with the Noetherian deﬁnition, and for which regular rings are Gorenstein, and coherent Gorenstein rings are Cohen-Macaulay. The relationship between Gorenstein rings and FP-injective dimension as deﬁned by Stenstrom is also explored. Finally, an additional characterization of Gorenstein rings involving homological dimensions is examined in the non-Noetherian case.