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General introduction Part I The Geometry of PU(2)-Instanton Moduli Spaces over Manifolds with Negative Definite Intersection Form Introduction 1 Preliminaries 1.1 The moduli space and invariants 1.2 SU(2), SO(3) and PU(2) moduli spaces 1.3 The moduli space of ASD-connections on a line bundle 1.4 Local model 1.5 Irreducibility 1.6 Regularity 1.7 Expected dimension 1.8 Compactness and orientability 1.9 Universal bundle and Donaldson u-classes 1.10 The parametrised moduli space 1.11 The Z2-metric 2 A problem in finite dimensional Riemannian geometry 2.1 The Groisser-Parker reduction 2.2 The problem 2.3 A slice of the action 2.4 The conical structure around the singular locus 2.5 The Sasaki metric in the total space of a vector bundle 2.6 The asymptotic of the metric 3 Index computations 3.1 Pontryagin classes and Donaldson ¦Ì-classes 3.2 Triviality of the projective bundle 4 Applications Part II Moduli Spaces of PU(2)-Instantons on Minimal Class VII Surfaces with b2=1 Introduction 1 Minimal class VII surfaces with b2=1 2 Filtrable holomorphic bundles 3 The local structure of the moduli space 4 Stability 5 The boundary of the moduli space of polystable bundles 6 Non-filtrable holomorphic bundles 7 The moduli spaces Acknowledgements Bibliography ±à¼­ÊÖ¼Ç