This is the complete X-ray source catalog of the ASCA Medium Sensitivity Survey, AMSS, or the Gas Imaging Spectrometer (GIS) catalog project. It has been constructed from data for fields covering Galactic latitudes |b| > 10 degrees which were obtained with the GIS instrument onboard the ASCA satellite between 1993 May and 1996 December (part I) and between 1997 January and 2000 May (part II). Part I of this catalog (AMSS-I) utilizes 368 combined fields, and contains 1343 sources (including target sources) with detection significance above 5 sigma in at least one of the 3 survey bands of 0.7-7.0, 2-10, or 0.7-2.0 keV, while AMSS-II uses 306 fields, and contains a total of 1190 sources, using the same criteria. The AMSS-I and AMSS-II catalogs together contain 2533 sources from an area of 278 square degrees and provide a unique database of X-ray sources in the flux range of 10^-13 to 10^-11 erg cm^-2 s^-1 (0.7-10 keV). The published paper contains a summary of the statistical properties of a complete X-ray sample consisting of 1969 serendipitous sources selected from AMSS-I and AMSS-II. For each source, the ASCA source name, position, 90% error radius, count rates (both observed and as corrected for Galactic absorption) in the 3 energy bands, detection signifances and fluxes in the 3 energy bands, and hardness ratio and associated error are provided. This version of the Browse ASCAGIS table containing the combined AMSS-I and AMSS-II source lists was created by the HEASARC in February 2006 based on the CDS version of the AMSS-I source list (CDS catalog J/ApJS/133/1) and the electronic ApJS version of the AMSS-II source list. This is a service provided by NASA HEASARC .