Lectures on Hyperbolic Geometry

Focussing On The Geometry Of Hyperbolic Manifolds, The Aim Here Is To Provide An Exposition Of Some Fundamental Results, While Being As Self-contained, Complete, Detailed And Unified As Possible. Following Some Classical Material On The Hyperbolic Space And The Teichmüller Space, The Book Centers On The Two Fundamental Results: Mostow's Rigidity Theorem (including A Complete Proof, Following Gromov And Thurston) And Margulis' Lemma. These Then Form The Basis For Studying Chabauty And Geometric Topology; A Unified Exposition Is Given Of Wang's Theorem And The Jorgensen-thurston Theory; And Much Space Is Devoted To The 3d Case: A Complete And Elementary Proof Of The Hyperbolic Surgery Theorem, Based On The Representation Of Three Manifolds As Glued Ideal Tetrahedra.