Preface.- Part I: Corrado Segre' Leadership: from Torino to the International Scene/Arena.- Contributions by Aldo Brigaglia, Alberto Conte and Livia Giacardi, Paola Gario, Erika Luciano and Clara Silvia Roero, David Rowe.- Part II: Perspectives on Segre's Legacy.- Contributions by Jérémy Blanc, Luca Chiantini and Duccio Sacchi, Ciro Ciliberto, Maria Angelica Cueto, Massimiliano Mella, Kristian Ranestad and Piotr Zwiernik, Laura Costa, Rosa M. Miró-Roig and Joan Pons-Llopis, Igor Dolgachev, Margarida Mendes Lopes and Rita Pardini, Emilia Mezzetti, Edoardo Sernesi.- Part III: The Unpublished Notebook of Corrado Segre Sulla Geometria Sugli Enti Algebrici Semplicemente Infiniti (1890-1891).- Alberto Conte, Introduction.- Reproduction of the Manuscript.- Appendices.