Vladimir N. Gribov, who died in 1997, was undoubtedly one of the key figures in theoretical physics not only in Russia but also abroad. Known mainly in the West for his contribution to field theory (e.g.the puzzling Gribov ambiguity) he also worked in the 1960s on the role of complex angular momenta in high energy particle physics, a subject he presented 1969 at length in a course at Leningrad (now St. Petersburg). Much later an English version of the Russian lecture notes was prepared and edited in this book to demonstrate the impact of the ideas of Regge, Chew-Frautschi, Sommerfeld-Watson, Mandelstam, Gribov-Froissart, Pomeranchuk, Landau and others on the scattering formalism, especially in a situation when the cross section stays constant at large energies. Though all this seems to be history, the calculational techniques developed in these pioneering days are still useful today, especially for analyzing hadron interactions at high energies. With this respect the now published summary is unique, important and impressive. Readers, however, should be familiar with Mandelstam’s double dispersion relation, Feynman rules and the basics of hadron physics.