This document describes the analysis done to extract the diphoton cross section for the run 1 dataset. The dataset, cuts, efficiencies, systematic error evaluation and final results are all covered. This document is being posted to provide a complete description of the analysis done in preparation for a final blessed result and a more succinct article. Posted to /cdf/pub/thesis/cdf5172_Diphoton_thesis.ps http://www-cdf.fnal.gov/thesis/cdf5172_Diphoton_thesis.ps Posted by rebcdf@cdfsga.fnal.gov