Contents: v.1. Properties and operations, by I. M. Gel'fand and generalized functions, by I. M. Gel'fand and G. E. Shilov, translated by M. D. Friedman, A. Feinstein and C. P. Peltzer. -v.3. Theory of differetial equantions, by I. M. Gel 'fand and G. E. Shilov translated by M.E.Mayer.-v.4.Applications of harmonic analysis, by I.M.Gel'fand and N.Ya.Vilenkin, translated by A.Feinstein.-v.5.Integral geometry and represetnation theory, by I.M.Gel'fand, M.I.Graev, and N.Ya. Vilenkin, translated by E.Saletan