  In this survey article, we recall some facts about split Kac-Moody groups as
defined by J. Tits, describe their main properties and then propose an analogue
of Borel-Tits theory for a non-split version of them. The main result is a
Galois descent theorem, i.e. the persistence of a nice combinatorial structure
after passing to rational points. We are also interested in the geometric point
of view, namely the production of new buildings admitting (nonuniform)
lattices.

Group Theory