one of the main themes of this book is the conflict betweenthe "flexibility' and the "rigidity properties of the hyperbolicmanifolds： the first radical difference arises between the case ofdimension 2 and the case of higher dimensions （as proved inchapters b and c）， an elementary feature of thus phenomenon beingthe difference between the riemann mapping theorem and liouville'stheorem， as pointed out in chapter a. thus chapter is ratherclementary and most of its material may' be the object of anundergraduate course.
together with the rigidity theorem， a basic tool for the study ofhyperbolic manifolds is margulis' lemma， a detailed proof of whichwe give in chapter d; as a consequence of this result in the samechapter we also give a rather accurate description， in alldimensions， of the thin-thick decomposition of a hyperbolicmanifold （especially in case of finite volume）.
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