Besson, G. The geometrization conjecture after R. Hamilton and G. Perelman. (English) Zbl 1150.53022 Rend. Semin. Mat., Univ. Politec. Torino 65, No. 4, 397-411 (2007). This beautiful paper describes the main ideas leading to the proof of the Poincaré and the Geometrization conjecture by G. Perelman using the Ricci flow defined by R. Hamilton. It is the written text of a Lagrange lecture given at Torino University, and contains many helpful graphics.The paper serves as a guide to the extensive bibliography. Reviewer: L. Del Riego (San Luis Potosí) MSC: 53C44 Geometric evolution equations (mean curvature flow, Ricci flow, etc.) (MSC2010) 53C21 Methods of global Riemannian geometry, including PDE methods; curvature restrictions 57M40 Characterizations of the Euclidean \(3\)-space and the \(3\)-sphere (MSC2010) Keywords:geometrization conjecture; Poincaré conjecture; Ricci flow; surgery; singularities PDFBibTeX XMLCite \textit{G. Besson}, Rend. Semin. Mat., Univ. Politec. Torino 65, No. 4, 397--411 (2007; Zbl 1150.53022)