  Unresolved and resolved sources of gravitational waves are at the origin of a
stochastic gravitational wave background. While the computation of its mean
density as a function of frequency in a homogeneous and isotropic universe is
standard lore, the computation of its anisotropies requires to understand the
coarse graining from local systems, to galactic scales and then to cosmology.
An expression of the gravitational wave energy density valid in any general
spacetime is derived. It is then specialized to a perturbed
Friedmann-Lema\^itre spacetime in order to determine the angular power spectrum
of this stochastic background as well as its correlation with other
cosmological probes, such as the galaxy number counts and weak lensing. Our
result for the angular power spectrum also provides an expression for the
variance of the gravitational wave background.
