  We generalize Sen theory to extensions $K_\infty/K$ whose Galois group is a
$p$-adic Lie group of arbitrary dimension. To do so, we replace Sen's space of
$K$-finite vectors by Schneider and Teitelbaum's space of locally analytic
vectors. One then gets a vector space over the field of locally analytic
vectors of $\hat{K}_\infty$. We describe this field in general and pay a
special attention to the case of Lubin-Tate extensions.
