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Non-lorentzian spacetimes

I review some of my recent work on non-lorentzian geometry. I review the classification of kinematical Lie algebras and their associated Klein geometries. I then describe the Cartan geometries modelled on them and their characterisation in terms of their intrinsic torsion. (To appear in the special issue "Applications of transformation groups" to be published by the Journal of Differential Geometry and Applications.)