Introductory Overview. - I. Observables and Pure States. - II. Quantization and the Classical Limit. - III. Groups Bundles and Groupoids. - IV. Reduction and Induction. - I Observables and Pure States. - 1 The Structure of Algebras of Observables. - 2 The Structure of Pure State Spaces. - 3 From Pure States to Observables. - II Quantization and the Classical Limit. - 1 Foundations. - 2 Quantization on Flat Space. - 3 Quantization on Riemannian Manifolds. - III Groups Bundles and Groupoids. - 1 Lie Groups and Lie Algebras. - 2 Internal Symmetries and External Gauge Fields. - 3 Lie Groupoids and Lie Algebroids. - IV Reduction and Induction. - 1 Reduction. - 2 Induction. - 3 Applications in Relativistic Quantum Theory. - Notes. - I. - II. - III. - IV. - References. Language: English