M.J.D. Hamilton has been teaching mathematics at all levels at Ludwig-Maximilians-Universität München and Universität Stuttgart for the past fifteen years. He is interested in the interactions of geometry and theoretical physics, and is known for his successful transfer of ideas between the two subjects. He is the author of the acclaimed textbook 'Mathematical Gauge Theory' (2017). D. Kotschick has been Professor of Mathematics, holding the Chair of Differential Geometry, at Ludwig-Maximilians-Universität München for twenty-five years. A researcher of exceptionally broad knowledge and interests, he is an internationally recognised expert in several areas of geometry and topology.  He is known for the depth and insight of his research as well as for his meticulous scholarship and the clarity of his writing. He is a long-standing member of the London Mathematical Society and in 1996 received the Lucien Godeaux Prize of the Royal Society of Liège.

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• 1. Introduction; 2. Linear algebra and bundle theory; 3. Symplectic geometry; 4. Foliations and connections; 5. Künneth structures; 6. The Künneth connection; 7. The curvature of a Künneth structure; 8. Hypersymplectic geometry; 9. Nilmanifolds; 10. Four-manifolds.