  Let $\Sigma$ be a hyperbolic surface. We study the set of curves on $\Sigma$
of a given type, i.e. in the mapping class group orbit of some fixed but
otherwise arbitrary $\gamma_0$. For example, in the particular case that
$\Sigma$ is a once-punctured torus, we prove that the cardinality of the set of
curves of type $\gamma_0$ and of at most length $L$ is asymptotic to $L^2$
times a constant.
