We present the first Fermi-Large Area Telescope (LAT) solar flare catalog covering the 24th solar cycle. This catalog contains 45 Fermi-LAT solar flares (FLSFs) with emission in the gamma-ray energy band (30 MeV-10 GeV) detected with a significance of >= 5 sigma over the years 2010-2018. A subsample containing 37 of these flares exhibits delayed emission beyond the prompt-impulsive hard X-ray phase, with 21 flares showing delayed emission lasting more than two hours. No prompt-impulsive emission is detected in four of these flares. We also present in this catalog observations of GeV emission from three flares originating from active regions located behind the limb of the visible solar disk. We report the lightcurves, spectra, best proton index, and localization (when possible) for all FLSFs. The gamma-ray spectra are consistent with the decay of pions produced by >300 MeV protons. This work contains the largest sample of high-energy gamma-ray flares ever reported and provides a unique opportunity to perform population studies on the different phases of the flare and thus allowing a new window in solar physics to be opened.
