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The Global Ultraviolet Imager (GUVI) onboard the Thermosphere-Ionosphere-Mesosphere Energetics and Dynamics (TIMED) satellite senses far ultraviolet emissions from O and N₂ in the thermosphere. Transformation of far ultraviolet radiances measured on the Earth limb into O, N₂, and O₂ number densities and temperature quantifies these responses and demonstrates the value of simultaneous altitude and geographic information. Composition and temperature variations are available from 2002 to 2007. This paper documents the extraction of these data products from the limb emission rates. We present the characteristics of the GUVI limb observations, retrievals of thermospheric neutral composition and temperature from the forward model, and the dramatic changes of the thermosphere with the solar cycle and geomagnetic activity. We examine the solar extreme ultraviolet (EUV) irradiance magnitude and trends through comparison with simultaneous Solar Extreme EUV (SEE) measurements on TIMED and find the EUV irradiance inferred from GUVI averaged (2002\textendash2007) 30\% lower magnitude than SEE version 11 and varied less with solar activity. The smaller GUVI variability is not consistent with the view that lower solar EUV radiation during the past solar minimum is the cause of historically low thermospheric mass densities. Thermospheric O and N₂ densities are lower than the NRLMSISE-00 model, but O₂ is consistent. We list some lessons learned from the GUVI program along with several unresolved issues.