This book presents the Projective approach to de Sitter Relativity. It traces the development of renewed interest in models of the universe at constant positive curvature such as -vacuum- geometry. The De Sitter Theory of Relativity, formulated in 1917 with Willem De Sitter's solution of the Einstein equations, was used in different fields during the 1950s and 1960s, in the work of H. Bacry, J.M. LevyLeblond and F.Gursey, to name some important contributors. From the 1960s to 1980s, L. Fantappie and G. Arcidiacono provided an elegant group approach to the De Sitter universe putting the...