  We define a new spectrum for compact length spaces and Riemannian manifolds
called the "covering spectrum" which roughly measures the size of the one
dimensional holes in the space. More specifically, the covering spectrum is a
set of real numbers $\delta>0$ which identify the distinct $\delta$ covers of
the space. We investigate the relationship between this covering spectrum, the
length spectrum, the marked length spectrum and the Laplace spectrum. We
analyze the behavior of the covering spectrum under Gromov-Hausdorff
convergence and study its gap phenomenon.
