Abstract : A symplectic Lie group is a Lie group endowed with a left invariant symplectic form. These groups are naturally endowed with an affine structure associted to a symplectic form.
In this thesis, on the one hand, we determine the $4$ and $6$-dimentional connected and simply connected symplectic Lie groups and on the other hand we study an infinity familly of symplectic groups in which the symplectic form is "invariantly" exact.
In all these cases we are interesting to the existence of the Lagrangian subgroups and sometimes transversal Lagrangian subgroups to underline left invariant symplectic affines structures.
The structure of these groups is studied using the momentum map