  In this paper, for a non compact and orientable surface $S$ been either: the
Infinite Loch Ness monster, the Cantor tree and the Blooming Cantor tree, we
construct explicitly an infinitely generated Fuchsian group
$\Gamma<PSL(2,\mathbb{R})$, such that the quotient $\mathbb{H}/\Gamma$ is a
hyperbolic surface homeomorphic to $S$.
