Contents  
1 Introduction  
2 Hyperbolic groups  
2.1 Classification of elements  
2.2 The Rips complex  
2.3 Subgroups  
2.4 Boundary  
2.5 Asymptotic dimension  
2.6 JSJ decomposition  
2.7 The Combination theorem  
2.8 Random groups are hyperbolic  
2.9 ℝ-trees and applications  
2.10 Hyperbolic spaces degenerate to ℝ-trees  
2.11 The Rips machine  
2.12 Applications  
3 Mapping class groups  
3.1 The boundary of the curve complex  
3.2 WPD, a cylindrically hyperbolic groups, quasi-morphisms  
3.3 Subsurface projections  
4 Projection complexes  
5 Out(Fₙ)  
5.1 Outer space  
5.2 The boundary of Outer space  
5.3 Lipschitz metric and train-track maps  
5.4 Hyperbolic complexes  
5.5 Subfactor projections  
5.6 Questions