In three years of observations since the beginning of nominal science operations in 2008 August, the Large Area Telescope (LAT) on board the Fermi Gamma-Ray Space Telescope has observed high-energy (≳ 20 MeV) γ-ray emission from 35 gamma-ray bursts (GRBs). Among these, 28 GRBs have been detected above 100 MeV and 7 GRBs above ∼20 MeV. The first Fermi-LAT catalog of GRBs is a compilation of these detections and provides a systematic study of high-energy emission from GRBs for the first time. To generate the catalog, we examined 733 GRBs detected by the Gamma-Ray Burst Monitor (GBM) on Fermi and processed each of them using the same analysis sequence. Details of the methodology followed by the LAT collaboration for the GRB analysis are provided. We summarize the temporal and spectral properties of the LAT-detected GRBs. We also discuss characteristics of LAT-detected emission such as its delayed onset and longer duration compared with emission detected by the GBM, its power-law temporal decay at late times, and the fact that it is dominated by a power-law spectral component that appears in addition to the usual Band model. © 2013. The American Astronomical Society. All rights reserved.