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Isodualité des réseaux 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 ${\bf SO}_0(p,q)$, ${\bf Sp}(2g,{\bf R})$ and ${\bf SU}(p,q)$. 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.