101 pages, 26 figures, accepted for publication in Astrophysical Journal Supplement Series. The ancillary files are PDFs of the full versions of Tables 4 and 8 and a FITS version of Table 11. v3 has corrected Table 6 and minor edits. The 3FGL catalog is available at http://fermi.gsfc.nasa.gov/ssc/data/access/lat/4yr_catalog ; International audience ; We present the third Fermi Large Area Telescope source catalog (3FGL) of sources in the 100 MeV-300 GeV range. Based on the first four years of science data from the Fermi Gamma-ray Space Telescope mission, it is the deepest yet in this energy range. Relative to the 2FGL catalog, the 3FGL catalog incorporates twice as much data as well as a number of analysis improvements, including improved calibrations at the event reconstruction level, an updated model for Galactic diffuse gamma-ray emission, a refined procedure for source detection, and improved methods for associating LAT sources with potential counterparts at other wavelengths. The 3FGL catalog includes 3033 sources above 4 sigma significance, with source location regions, spectral properties, and monthly light curves for each. Of these, 78 are flagged as potentially being due to imperfections in the model for Galactic diffuse emission. Twenty-five sources are modeled explicitly as spatially extended, and overall 232 sources are considered as identified based on angular extent or correlated variability (periodic or otherwise) observed at other wavelengths. For 1009 sources we have not found plausible counterparts at other wavelengths. More than 1100 of the identified or associated sources are active galaxies of the blazar class; several other classes of non-blazar active galaxies are also represented in the 3FGL. Pulsars represent the largest Galactic source class. From source counts of Galactic sources we estimate the contribution of unresolved sources to the Galactic diffuse emission is ~3% at 1 GeV.