  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.
