This proceedings contains tutorials presented at the NATO Advanced Study Institute on Design and Implementation of Optimiz­ ation Software (Urbino, Italy, 20 June - 2 July, 1977) organized by the Committee on Algorithms (COAL) of the Mathematical Program­ ming Society. The authors are to be congratulated on their clear expositions plus their prompt cooperation. We were especially fortunate to have had two of the first pioneers in designing mathematical programming systems: W. Orchard-Hays and E. M. L. Beale. Surveying the contents the reader will find that the papers fall into three categories which we can roughly designate by: linear programming, extensions of linear programming, and non­ linear programming. In the first category on linear programming, the three back­ ground papers by W. Orchard-Hays capture a historical perspective through the scope of modern systems, while T. J. Dekker's paper provides background in numerical methods used in optimization software. One area neglected by most previous mathematical pro­ gramming symposia is the information structure employed to mani­ pulate large volumes of data. The tutorial on matricial packing by H. J. Greenberg includes modern structures, including recent suggestions by J. Kalan and D. Rarick; another tutorial on pivot selection describes the vast range of tactics that have evolved, aimed at reducing computational effort with the strategy of the simplex method.