  This article presents some methods to control the bottom of the spectrum of
the Laplacian $\lambda_0$ on hyperbolic surfaces with infinite volume. Our
first result bounds the $\lambda_0$ of a geometrically finite surface in terms
of the geometry of its convex core. We then focus on infinite type periodic
hyperbolic surfaces built by gluing copies of a geometrically finite surface
with boundary according to the plan of an infinite graph. We control the
$\lambda_0$ of the so-obtained infinite surfaces by constants coming from
spectral properties of the building brick and combinatorial datae of the graph.
We then use these methods to control the $\lambda_0$ of two other kind of
infinite type hyperbolic surfaces : those admitting a splitting into bounded
pieces, and some riemannian coverings.
