Thisbookisintendedasanintroductiontofixedpointtheoryanditsapplications.Thetopicstreatedrangefromfairlystandardresults（suchasthePrincipleofContractionMapping，BrouwersandSchaudersfixedpointtheorems）tothefrontierofwhatisknown，butwehavenottriedtoachievemaximalgeneralityinallpossibledirections.Wehopethatthereferencesquotedmaybeusefulforthispurpose.　　Thepointofviewadoptedinthisbookisthatoffunctionalanalysis;forthereadersmoreinterestedinthealgebraictopologicalpointofviewwehaveaddedsomereferencesattheendofthebook.Aknowledgeoffunctionalanalysisisnotaprerequisite，althoughaknowledgeofanintroductorycourseinfunctionalanalysiswouldbeprofitable.However，thebookcontainstwointroductorychapters，oneongeneraltopologyandanotheronBanachandHilbertspaces.