This 12-volume index, when used in conjunction with other published author and subject cumulative indexes and Mathematical Reviews Annual Indexes, provides complete indexes for the entire run of MR from its beginning in 1940 through the present. This index contains both author and subject listings for the (approximately) 200,000 reviews published during 1980-1984 and for another 8,000 papers not reviewed individually by MR. The author index offers complete bibliographic information for each item and gives cross-references. Under each area, the subject index contains a listing for each item reviewed that was given either a primary or secondary classification in the area according to the 1980 Mathematics Subject Classification.