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We describe the automated spectral classification, redshift determination, and parameter measurement pipeline in use for the Baryon Oscillation Spectroscopic Survey (BOSS) of the Sloan Digital Sky Survey UI (SDSS-III) as of the survey's ninth data release (DR9), encompassing 831,000 moderate-resolution optical spectra. We give a review of the algorithms employed, and describe the changes to the pipeline that have been implemented for BOSS relative to previous SDSS-I/II versions, including new sets of stellar, galaxy, and quasar redshift templates. We test the accuracy of these statistical redshift error estimates using repeat observations, finding them underestimated by a factor of 1.19-1.34 for galaxies and by a factor of two for quasars. We assess the impact of sky-subtraction quality, signal-to-noise ratio, and other factors on galaxy redshift success. Finally, we document known issues with the BOSS DR9 spectroscopic data set and describe directions of ongoing development