We discuss the notion of duality and self-duality in the context of the dua
l projection operation that creates an internal space of potentials. Distin
ctly from the algebraic or group theoretical methods, this technique is app
licable to both even and odd dimensions. The parity in the kernel of the Ga
uss law is shown to play a crucial role in determining the dimensional depe
ndence of the duality groups and actions, Using this novel concept, we deri
ve the appropriate invariant actions and discuss the symmetry groups and th
eir proper generators. In particular, the presence of a duality symmetry an
d self-duality in Maxwell theory in 2+1 dimensions is analyzed in details.
The corresponding action is a 3D version of the familiar duality symmetric
electromagnetic theory in 4D. Finally, the duality symmetric actions in the
different dimensions constructed here manifest both the SO(2) and Z(2) sym
metries, contrary to conventional results.