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.<br /> 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. <br />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.<br />The structure of these groups is studied using the momentum map