Oneofthemainthemesofthisbookistheconflictbetweenthe"flexibility'andthe"rigiditypropertiesofthehyperbolicmanifolds：thefirstradicaldifferencearisesbetweenthecaseofdimension2andthecaseofhigherdimensions（asprovedinchaptersBandC），anelementaryfeatureofthusphenomenonbeingthedifferencebetweentheRiemannmappingtheoremandLiouville'stheorem，aspointedoutinchapterA.Thuschapterisratherclementaryandmostofitsmaterialmay'betheobjectofanundergraduatecourse.　　Togetherwiththerigiditytheorem，abasictoolforthestudyofhyperbolicmanifoldsisMargulis'lemma，adetailedproofofwhichwegiveinchapterD;asaconsequenceofthisresultinthesamechapterwealsogivearatheraccuratedescription，inalldimensions，ofthethin-thickdecompositionofahyperbolicmanifold（especiallyincaseoffinitevolume）.