Cosmic topology: Twenty years after

What is the shape of the Universe? Is it finite or infinite ? Is space multi-connected to create ghost images of faraway cosmic sources? After a "dark age" period, the field of cosmic topology has now become one of the major concerns in astronomy and cosmology, not only from theorists but also from observational astronomers. Here I give a personal account of the spectacular progress in the field since the beginning of the 1990's, when I started to work in it.
14 pages. Contribution to a special issue of the journal "Gravitation and Cosmology" devoted to the 75th birthday of Prof. Andrey Grib. Version 2 (some sentences have been rephrased to avoid text overlap with arXiv:1303.5086, arXiv:1303.4226, arXiv:1104.0015 by other authors). arXiv admin note: text overlap with arXiv:0802.2236