I describe studies done by the theory group of Lebedev Physical Institute in Moscow and point out the cross-influence of some of our work with that of Rolf Hagedorn, and show how this research continued and evolved up to the present. 9.1 The Beginning Cosmic Rays and Landau High energy hadron interactions were always one of the main topics of research at the Moscow Lebedev Physical Institute. On the experimental side, cosmic ray studies which started already in the 1930s were quite successful. The interest in high energy studies further increased after construction of first accelerator at the Institute with active participation of V.I. Veksler who soon proposed the autofocusing concept (1944) and moved to Dubna with many collaborators to realize his visions and build accelerators. In parallel, theoretical work became more intense. Many researchers became excited seeing L.D. Landau paper on the hydrodynamic model of hadron interactions in 1953 [1]. Landau used to say that the work on it was the most hard, and time-consuming compared to all other of his papers. Actually, it was the first one which contained the detailed calculations ascribing the macroscopic features to the microscopic objects along the line of thought initiated by E. Fermi in 1950. At that time, in my 3rd graduate year, I devoted several days to studying Landau's paper in the Moscow Polytechnic library. Landau's approach was widely discussed by theorists at LPI. Hydrodynamic equations were further analyzed by E.L. Feinberg, D.S. Chernavsky and G.A. Milekhin. They published a series of papers on this topic in the 1950s. This