sci The FInite element Automatic Tabulator FIAT supports generation of arbitrary order instances of the Lagrange elements on lines, triangles, and tetrahedra. It is also capable of generating arbitrary order instances of Jacobi-type quadrature rules on the same element shapes. Further, H(div) and H(curl) conforming finite element spaces such as the families of Raviart-Thomas, Brezzi-Douglas-Marini and Nedelec are supported on triangles and tetrahedra. Upcoming versions will also support Hermite and nonconforming elements.