The Large Area Telescope (LAT) aboard the $Fermi$ spacecraft routinely observes high-energy emission from gamma-ray bursts (GRBs). Here we present the second catalog of LAT-detected GRBs, covering the first 10 years of operations, from 2008 August 4 to 2018 August 4. A total of 186 GRBs are found; of these, 91 show emission in the range $30-100,$MeV (17 of which are seen only in this band) and 169 are detected above 100 MeV. Most of these sources were discovered by other instruments ($Fermi$/GBM, $Swift$/BAT, AGILE, INTEGRAL) or reported by the Interplanetary Network (IPN); the LAT has independently triggered on 4 GRBs. This catalog presents the results for all 186 GRBs. We study onset, duration and temporal properties of each GRB, as well as spectral characteristics in the $100,$MeV$-100,$GeV energy range. Particular attention is given to the photons with highest energy. Compared with the first LAT GRB catalog, our rate of detection is significantly improved. The results generally confirm the main findings of the first catalog: the LAT primarily detects the brightest GBM bursts, and the high-energy emission shows delayed onset as well as longer duration. However, in this work we find delays exceeding 1 ks, and several GRBs with durations over 10 ks. Furthermore, the larger number of LAT detections shows that these GRBs cover not only the high-fluence range of GBM-detected GRBs, but also samples lower fluences. In addition, the greater number of detected GRBs with redshift estimates allows us to study their properties in both the observer and rest frames. Comparison of the observational results with theoretical predictions reveals that no model is currently able to explain all results, highlighting the role of LAT observations in driving theoretical models.
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