Can the CMB reveal the topology of the universe?

This article summarizes recent progress in the development of tools to study the topology of the universe with the cosmic microwave background. The different signatures of the topology and observational constraints are described. The ability of future experiments to reveal the topological structure of our universe is then discussed. To cite this article: J.P. Uzan, A. Riazuelo, C. R. Physique 4 (2003).