This paper describes the operational version 3 algorithms used to analyze data from the Polar Ozone and Aerosol Measurement (POAM) III instrument. We include a thorough discussion of both the forward model and retrieval algorithms, including the algorithms used to derive altitude information and normalize the measured radiances to produce atmospheric transmission profiles. The operational POAM III algorithms retrieve O3, NO2, H2O, and O2 (or total) density, as well as aerosol extinction between 353 and 1018 nm. All atmospheric species are retrieved simultaneously using the technique of optimal estimation. The conversion of transmission data to geophysical profiles is achieved via a two-step process, beginning with a spectral inversion to partition the various gas and aerosol components of the measured slant optical depth, followed by a spatial inversion to produce altitude profiles of gas density and aerosol extinction from the path-integrated quantities. A formal error analysis is also presented, yielding estimates of the total random error budget for the retrieved profiles. In addition to the theoretical error analysis, we present results from empirical analyses that quantify error components due to aerosol feedback in the gas retrievals, as well as sunspot artifacts that are sometimes present in the data. Finally, we present a quantitative retrieval characterization based on analysis of the full retrieval averaging kernel matrix. This matrix is used to calculate vertical resolution profiles for all retrieved species, as well as to quantify the information content of the retrievals, including the a priori weighting in the retrievals, the coupling between the various retrieval species, and the spectral resolution of the aerosol retrievals.