A summary of the results obtained for a new comprehensive geodetic parameter solution from the analysis of LAGEOS laser ranging data for the period May 1976 to the end of 1982 is presented. Estimates of each component of the polar motion and earth rotation, the station coordinates, the value of the earth's gravitational constant GM, and the elements of the LAGEOS orbit comprise this SL5.1AP solution. The results differ from previously published values primarily through incorporation of more rigorous dynamic models for the ocean and solid earth tides. The precision of the geodetic parameters are on average 5-marc sec polar motion, 0.2-ms length of day, better than 5-cm center-of-mass geodetic positioning, 3-cm global baselines, and 2-cm regional baselines. An assessment of the contribution of systematic errors in the interstation distance determination is presented.