Thisbook,whichbeganasaseminarin1985atMIT,containscompleteproofsofthelocalindextheoremforDiracoperatorsusingtheheatkernelapproach,togetherwithitsgeneralizationstoequivariantDiracoperatorsandfamiliesofDiracoperators,aswellasbackgroundmaterialonsuperconnectionsandequivariantdifferentialforms.
Sincethepublicationofthefirstedition,thesubjectstreatedherehavecontin-uedtofindnewapplications.Equivariantcohomologyplaysanimportantroleinthestudyofsymplecticreduction,andBismutsuperconnectionsandthelocalindexthe-oremforfamilieshavehadmanyapplications,throughtheconstructionofhigheranalytictorsionformsandcurrents.(Forasurveyofsomeofthesedevelopments,werecommendreadingBismutstalkattheBerlinInternationalCongressofMathe-maticians,reference
Althoughthisbooklackssomeoftheusualattributesofatextbook(suchasexercises),ithasbeenwidelyusedinadvancedcoursesindifferentialgeometry;formanyofthetopicsdiscussedhere,therearenoothertreatmentsavailableinmonographform.Becauseofthecontinuingdemandfromstudentsforthebook,wewerevery