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We present systematic spectral analyses of GRBs detected with the Burst and Transient Source Experiment (BATSE) onboard the Compton Gamma-Ray Observatory (CGRO) during its entire nine years of operation. This catalog contains two types of spectra extracted from 2145 GRBs and fitted with five different spectral models resulting in a compendium of over 19000 spectra. The models were selected based on their empirical importance to the spectral shape of many GRBs, and the analysis performed was devised to be as thorough and objective as possible. We describe in detail our procedures and criteria for the analyses, and present the bulk results in the form of parameter distributions. This catalog should be considered an official product from the BATSE Science Team, and the data files containing the complete results are available from the High-Energy Astrophysics Science Archive Research Center (HEASARC).