  Duality symmetries of supergravity theories are powerful tools to restrict
the number of possible actions, to link different dimensions and number of
supersymmetries and might help to control quantisation.
(Hodge-Dirac-)Dualisation of gauge potentials exchanges Noether and topological
charges, equations of motion and Bianchi identities, internal rigid symmetries
and gauge symmetries, local transformations with nonlocal ones and most
exciting particles and waves. We compare the actions of maximally dualised
supergravities (ie with gauge potential forms of lowest possible degree) to the
non-dualised actions coming from 11 (or 10) dimensions by plain dimensional
reduction as well as to other theories with partial dualisations. The effect on
the rigid duality group is a kind of contraction resulting from the elimination
of the unfaithful generators associated to the (inversely) dualised scalar
fields. New gauge symmetries are introduced by these (un)dualisations and it is
clear that a complete picture of duality (F(ull)-duality) should include all
gauge symmetries at the same time as the rigid symmetries and the spacetime
symmetries. We may read off some properties of F-duality on the internal rigid
Dynkin diagram: field content, possible dualisations, increase of the rank
according to the decrease of space dimension... Some recent results are
included to suggest the way towards unification via a universal twisted
self-duality (TS) structure. The analysis of this structure had revealed
several profound differences according to the parity mod 4 of the dimension of
spacetime (to be contrasted with the (Bott) period 8 of spinor properties).
