We present the second AGILE-GRID catalogue (2AGL) of gamma-ray sources in the energy range 100MeV-10GeV. With respect to previous AGILE-GRID catalogues, the current 2AGL catalogue is based on the first 2.3 years of science data from the AGILE mission (the so-called pointing mode) and incorporates more data and several analysis improvements, including better calibrations at the event reconstruction level, an updated model for the Galactic diffuse gamma-ray emission, a refined procedure for point-like source detection, and the inclusion of a search for extended gamma-ray sources. The 2AGL catalogue includes 175 high-confidence sources (above 4{sigma} significance) with their location regions and spectral properties and a variability analysis with four-day light curves for the most significant. Relying on the error region of each source position, including systematic uncertainties, 122 sources are considered as positionally associated with known counterparts at different wavelengths or detected by other gamma-ray instruments. Among the identified or associated sources, 62 are active galactic nuclei (AGNs) of the blazar class. Pulsars represent the largest Galactic source class, with 41 associated pulsars, 7 of which have detected pulsation; 8 supernova remnants and 4 high-mass X-ray binaries have also been identified. A substantial number of 2AGL sources are unidentified: for 53 sources no known counterpart is found at different wavelengths. Among these sources, we discuss a subclass of 29 AGILE-GRID-only gamma-ray sources that are not present in 1FGL, 2FGL, or 3FGL catalogues; the remaining sources are unidentified in both 2AGL and 3FGL catalogues. We also present an extension of the analysis of 2AGL sources detected in the energy range 50-100MeV.