The aim of this book is to give a proof of Thurston's Geometrisation Conjecture, solved by G. Perelman in 2003. Perelman's work completes a program initiated by R. Hamilton, using a geometric evolution equation called Ricci flow. Perelman presented his ideas in three very concise manuscripts [Per02], [Реr03a], [Реr03b]. Important work has since been done to fill in the details. The first set of notes on Perelman's papers was posted on the web in June 2003 by B. Kleiner and J. Lott. These notes have progressively grown to the point where they cover the two papers [Per02], [Реr03b]...