This report presents a summary of the results, obtained during the period of 1955 to 1960, of studies of hypersonic flow problems carried out at the Rensselaer Polytechnic Institute. The problesm investigated are: (1) Effect of free stream vorticity on laminar boundary layer flow, (2) Hypersonic flow field around blunt bodies, (3) Real gas effects in hypersonic flows, (4) An inverse problem in hypersonic viscous flow, (5) Some studies of unsteady hypersonic flow phenomena, and (6) Hypersonic leading edge problem. Considerable progress has bee made in the understanding of these problems. These results are summarized in the present report. In the study of the real gas effects in hypersonic flows, considerable further work is necessary for a basic understanding of the nonequilibrium flow effects.