  This article describes the computation of cosmic microwave background
anisotropies in a universe with multi-connected spatial sections and focuses on
the implementation of the topology in standard CMB computer codes. The key
ingredient is the computation of the eigenmodes of the Laplacian with boundary
conditions compatible with multi-connected space topology. The correlators of
the coefficients of the decomposition of the temperature fluctuation in
spherical harmonics are computed and examples are given for spatially flat
spaces and one family of spherical spaces, namely the lens spaces. Under the
hypothesis of Gaussian initial conditions, these correlators encode all the
topological information of the CMB and suffice to simulate CMB maps.
