The notion of $n$-ary algebras, that is vector spaces with a multiplication
concerning $n$-arguments, $n \geq 3$, became fundamental since the works of
Nambu. Here we first present general notions concerning $n$-ary algebras and
associative $n$-ary algebras. Then we will be interested in the notion of
$n$-Lie algebras, initiated by Filippov, and which is attached to the Nambu
algebras. We study the particular case of nilpotent or filiform $n$-Lie
algebras to obtain a beginning of classification. This notion of $n$-Lie
algebra admits a natural generalization in Strong Homotopy $n$-Lie algebras in
which the Maurer Cartan calculus is well adapted.