  This thesis deals with the construction of conserved charges for
asymptotically flat spacetimes at spatial infinity in four spacetime dimensions
in a hopefully pedagogical way. As a first motivation of this work, it
highlights the difficulties one encounters when trying to understand the
gravitational duality, present at the linearized level, in the full non-linear
Einstein's theory or even just in an asymptotic regime of it. In the first
part, we restrict the discussion to the Noetherian surface charges, called
"electric charges", and study the existence of a larger phase space, than
previously known in the literature, where the awkward parity boundary
conditions, firstly imposed by T. Regge and C. Teitelboim, are relaxed. In the
absence of these parity conditions, we show how the Einstein-Hilbert action is
a correct variational principle when it is supplemented by an anomalous
counter-term and construct conserved and finite charges associated to the
larger asymptotic symmetry group. The second and third parts focus on the
magnetic information obtained through gravitational duality. As this duality is
only known at the linearized level, asymptotic linearity is implicitly assumed
at spatial infinity. In the second part, gravitational duality for the
linearized gravity theory is reviewed and ten dual Poincar\'e charges, or
topological "magnetic" charges, are constructed \`a la Abbott-Deser. The last
part explains how the NUT charge N, gravitational dual of the mass M and
present in the BPS bound of the supersymmetric charged Taub-NUT black hole,
copes with the N=2 superalgebra. This is achieved through a complexification of
the Witten-Nester 2-form.
