Thepresentbookstrivesforclarityandtransparency.Rightfromthebegin-ning，itrequiresfromthereaderawillingnesstodealwithabstractconcepts，aswellasaconsiderablemeasureofself-initiative.Forthesee&，rts，thereaderwillberichlyrewardedinhisorhermathematicalthinkingabilities，andwillpossessthefoundationneededforadeeperpenetrationintomathematicsanditsapplications.　　Thisbookisthefirstvolumeofathreevolumeintroductiontoanalysis.Itde-velopedfrom.coursesthattheauthorshavetaughtoverthelasttwentysixyearsattheUniversitiesofBochum，Kiel，Zurich，BaselandKassel.Sincewehopethatthisbookwillbeusedalsoforself-studyandsupplementaryreading，wehaveincludedfarmorematerialthancanbecoveredinathreesemestersequence.Thisallowsustoprovideawideoverviewofthesubjectandtopresentthemanybeautifulandimportantapplicationsofthetheory.Wealsodemonstratethatmathematicspossesses，notonlyeleganceandinnerbeauty，butalsoprovidesefficientmethodsforthesolutionofconcreteproblems.