• What is connection: falling cat, finances, and other simple examples
• Covariant derivative on Riemannian manifolds (ancient stuff)
• Cartan's method
• Koszul's description of connection
• Ehressman's approasch
• Connection without Lie groups !
  (All ---> from covariant derivative to parallel transport to curvature)
• Connection with Lie groups
• More examples:
  • geometric quantization
  • dust observers in space-time
  • gauge theories
• Gauge theory versus Kaluza-Klein model
• Berry phase - why so fashionable
• etc --- please give your suggestions

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