  We give a concise summary of the para-Hermitian geometry that describes a
doubled target space fit for a covariant description of T-duality in string
theory. This provides a generalized differentiable structure on the doubled
space and leads to a kinematical setup which allows for the recovery of the
physical spacetime. The picture can be enhanced to a Born geometry by including
dynamical structures such as a generalized metric and fluxes which are related
to the physical background fields in string theory. We then discuss a
generalization of the Levi-Civita connection in this setting - the Born
connection - and twisting of the kinematical structure in the presence of
fluxes.
