We made 22 observations on the Small Magellanic Cloud (SMC) and covered full regions of the main body and the eastern wing by the end of the ASCA mission. We detected 106 discrete sources with a criterion of S/N>5 and performed systematic analyses on all of the sources. We determined the source positions with an ~40" error radius (90% confidence) for sources detected in the central 20' radius of the GIS. We detected coherent pulsations from 17 sources. Among them, eight were newly discovered during this study. We classified most of these pulsars as X-ray binary pulsars (XBPs) based on their properties, such as the flux variability and the existence of an optical counterpart. We detected X-ray emission from eight supernova remnants (SNRs). Based on these ASCA results and further information from ROSAT, SAX, RXTE, CGRO, Chandra, and XMM-Newton, we compiled comprehensive catalogues of discrete X-ray sources in the Small Magellanic Cloud.