In1970IgaveagraduatecourseinergodictheoryattheUniversityofMarylandinCollegePark,andtheselectureswerethebasisoftheSpringerLectureNotesinMathematicsVolume458called"ErgodicTheory--IntroductoryLectures"whichwaspublishedin1975.Thisvolumeisnowoutofprint,soIdecidedtoreviseandaddtothecontentsofthesenotes.Ihaveupdatedtheearlierchaptersandhaveaddedsomenewchaptersontheergodictheoryofcontinuoustransformationsofcompactmetricspaces.Inparticular,Ihaveincludedsomematerialontopologicalpressureandequilibriumstates.Inrecentyearstherehavebeensomefascinatinginteractionsofergodictheorywithdifferentiabledynamics,differentialgeometry,numbertheory,vonNeumannalgebras,probabilitytheory,statisticalmechanics,andothertopics.InChapter101havebrieflydescribedsomeoftheseandgivenreferencestosomeoftheothers.Ihopethatthisbookwillgivethereaderenoughfoundationtotackletheresearchpapersonergodictheoryanditsapplications.