Isodualit\'e des r\'eseaux euclidiens en petite dimension

We propose an algebraic and a geometric classification of euclidean isodual lattices of fixed rank. First, we prove that these lattices are distribued according to a finite number of algebraic types. Second, we show that they are parametrized by a finite number of symmetric spaces associated to the classical groups ${\mathbf{S}\mathbf{O}}_0(p,q)$, $\mathbf{S}\mathbf{p}(2g,\mathbf{R})$ and $\mathbf{S}\mathbf{U}(p,q)$. We obtain a complete discription of algebraic types and Gram matrices of isodual lattices up to rank 7. The maximal density problem is also discussed.