We construct exceptional field theory for the duality group
SL(3)×SL(2). The theory is defined on a space with 8 `external'
coordinates and 6 `internal' coordinates in the (3,2) fundamental
representation, leading to a 14-dimensional generalized spacetime. The bosonic
theory is uniquely determined by gauge invariance under generalized external
and internal diffeomorphisms. The latter invariance can be made manifest by
introducing higher form gauge fields and a so-called tensor hierarchy, which we
systematically develop to much higher degree than in previous studies. To this
end we introduce a novel Cartan-like tensor calculus based on a covariant
nil-potent differential, generalizing the exterior derivative of conventional
differential geometry. The theory encodes the full D=11 or type IIB
supergravity, respectively.Comment: 49 page