A bstract Double Field Theory (DFT) is an attempt to make the O ( d, d ) T-duality symmetry of string theory manifest, already before reducing on a -torus. It known that supergravity can be formulated in D, D covariant way, and remarkably this remains true first order ?? . We set up systematic way analyze invariants, working by fields, which we carry out 3 At recover Riemann squared invariant, ...