Thisisacompletelyrevisededition,withmorethanfiftypagesofnewmaterialscatteredthroughout.Inkeepingwiththeconventionalmeaningofchaptersandsections,Ihavereorgaruzedthebookintotwenty-ninesectionsinsevenchapters.ThemainadditionsareSection200ntheLiederivativeandinteriormultiplication,twointrinsicoperationsonamanifoldtooimportanttoleaveout,newcriteriainSection21fortheboundaryorientation,andanewappendixonquaternionsandthesymplecticgroup.
Apartfromcorrectingerrorsandmisprints,Ihavethoughtthrougheveryproofagain,clarifiedmanypassages,andaddednewexamples,exercises,hints,andsolutions.Intheprocess,everysectionhasbeenrewritten,sometimesquitedrastically.Therevisionsaresoextensivethatitisnotpossibletoenumeratethemallhere.Eachchapternowcomeswithanintroductoryessaygivinganoverviewofwhatistocome.Toprovideatimelineforthedevelopmentofideas,Ihaveindicatedwheneverpossi-blethehistoricaloriginoftheconcepts,andhaveaugmentedthebibliographywithhistoricalreferences.