Partoverstandardeneralropertiesfepresentationsfompactgroupsincludingieroupsndtherompactroups,uchsiniter-adienes）.hesencludechurrthogonality,ropertiesfatrixoefficientsandheeter-Weylheorem.PartIoversheundamentalsfieronps,yhicheanhoseub-jectshathinkreostrgentorhetudentoearn.hesencludehefollowingopicsorompactroups:heundamentalroup,heonjngacyofaximaloritworoofs）,ndheeylharacterormula.oroncom-pactroups,etartithomplexnalyticroupshatrebtainedycomplexificationfompactieroups,btaininghewasawandruhatdecompositions.hesercheeductiveomplexroups.heyrefoursespecialase,ntoodlaceotartnheoncompactorld.oreeneralnoncompactieroupsithartanecompositionretudiednheastfewhaptersfartI.hapter1,nymmetricpaces,lternatesxampleswithheory,iscussinghembeddingfoncompactymmetricpacenitsompactnal,heoundaryomponentsndergman-Shilovoundaryofymmetricubeomain,ntiartan\'slassification.hapter2on-structsheelativeootystem,xplainsatakeiagramsndivesxamplesillustratinghearioushenomenahatanccur,ndeproveshewasawadecomposition,ormerlybtainedoromplexnalyticroups,nhisoregeneralontext.inally,hapter3urveysheifferentaysieroupsanbembeddednuenother.

Prefaceart:ompactroupsaareasurechurrthogonalityompactperatorsheeter-Weylheoremart:ieroupundamentalsieubgroupsfL(n,)ectorieldseft-Invariantectorieldshexponentialapensorsndniversalroperties0heniversalnvelopinglgebra1xtensionfcalars2epresentationsf1(2,)3heniversalover4heocalrobeniusheorem5ori6eodesicsndaximalori7opologicalrooffartan\'sheorem8heeylntegrationormula9heootystem0xamplesfootystems1bstracteylroups2heundamentalroup3emisimpleompactroups4ighest-Weightectors5heeylharacterormula6pin7omplexification8oxeterroups9hewasawaecomposition0heruhatecomposition1ymmetricpaces2elativeootystems3mbeddingsfieroupsart:opics4ackeyheory5haractersfL(n,C)6ualityetweenkndL(n,C)7heacobi-Trudidentity8churolynomialsndL(n,C)9churolynomialsndk0andomatrixheory1inorsfoeplitzatrices2ranchingormulaendableaux3heauchydentity4nitaryranchingules5henvolutionodelork6omeymmetriclgebras7elfandairs8eckelgebras9hehilosophyfusporms0ohomologyfrassmannianseferencesndex