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APOLLO forward models the radiative transfer of light through a planetary (or brown dwarf) atmosphere; it also forward models transit and emission spectra and retrieves atmospheric properties of extrasolar planets. The code has two operational modes: one to compute a planetary spectrum given a set of parameters, and one to retrieve those parameters based on an observed spectrum. The package uses emcee (ascl:1303.002) to find the best fit to a spectrum for a given parameter set. APOLLO is modular and offers many options that may be turned on and off, including the type of observations, a flexible molecular composition, multiple cloud prescriptions, multiple temperature-pressure profile prescriptions, multiple priors, and continuum normalization.