Infinite-Dimensional Lie Theoryfor Gauge GroupsVom Fachbereich Mathematikder Technischen Universit¨at Darmstadtzur Erlangung des Grades eines Doktors derNaturwissenschaften (Dr. rer. nat.) genehmigteDissertationvonDipl.-Math. Christoph Wockelaus KasselReferent: Prof. Dr. Karl-Hermann NeebKorreferent: Prof. Dr. Peter MichorTag der Einreichung: 12.07.2006Tag der mundlic¨ hen Prufung¨ : 20.10.2006Darmstadt 2006D17To my parentsfor teaching me poems and fishesAcknowledgementI would like to express my gratitude to the people who supported me during my time as aPh.D. student. First of all I want to thank my advisor, Prof. Dr. Karl-Hermann Neeb, for hisexemplarysupervisionduringtheentiretime–forhisconstantavailability,outstandingscientificexpertise, a very good personal relationship, and active support of my scientific growth.Furthermore, I want to express my thanks to those members of the research group Algebra,Geometry and Functional Analysis at the mathematics department of the Technical Universityof Darmstadt who had an essential part in the formation of this thesis. In particular, I wantto thank Christoph Mul¨ ler for collaboration in all respects and for extensive proof reading, aswell as Helge G¨ockner for frequent consultation. For help in all administrative efforts during thework on this thesis I want to express my gratitude to Gerlinde Gehring. Further, I thank thewhole group for a friendly working atmosphere.