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The general theory of attaining enhanced transverse mode discrimination in an unstable ring resonator by employing an intracavity spatial fiber is developed. The theory presented is for the passive cavity mode structures of both the forward and reverse traveling wave fields supported by the optical cavity. Of particular interest here is the transverse mode behavior in the presence of strong spatial filtering wherein the spatial filter aperture completely dominates the diffractive mode structure formation processes. Both a circular focal point aperture and a pair of orthogonal focal line apertures are considered. The succeeding parts to this first paper describes the numerical and experimental results obtained for several unstable ring laser geometries with intracavity spatial filtering. The analysis presented here provides the fundamental understanding of these results.