In August 1981 the International Association of Geomagnetism and Aeronomy revised the International Geomagnetic Reference Field (IGRF). It is the second revision since the inception of the IGRF in 1968. The revision extends the earlier series of IGRF models from 1980 to 1985, introduces a new series of definitive models for 1965-1975, and defines a provisional reference field for 1975-1980. The revision consists of: (1) a model of the main geomagnetic field at 1980.0, not continuous with the earlier series of IGRF models, together with a forecast model of the secular variation of the main field during 1980-1985; (2) definitive models of the main field at 1965.0, 1970.0, and 1975.0, with linear interpolation of the model coefficients specified for intervening dates; and (3) a provisional reference field for 1975-1980, defined as the linear interpolation of the 1975 and 1980 main-field models. The new models are series of solid spherical harmonics up to and including the tenth degree and order for the main-field models, and up to and including the eighth degree and order for the secular variation model. The models were derived from three sets of proposed models by taking weighted means. The weights were chosen according to the apparent accuracy of the proposed models. A brief history of the IGRF, a review of basic formulas, and a set of world contour maps of the geomagnetic elements based on the IGRF 1980 model are included.