image of the composed map from the building to the compact space of (homothety classes of) seminorms on the non-Archimedean representation space.

For a given group, these two methods lead to the same family of compactifications, indexed by the conjugacy classes of parabolic subgroups. One interesting point in these two approaches is the fact that the compactifications are obtained by taking the closure of images of equivariant maps. The construction of the latter maps is also one of the main difficulties; it is overcome thanks to the fact that Berkovich geometry has a rich formalism which combines techniques from algebraic and analytic geometry (the possibility to use field extensions, or the concept of Shilov boundary, are for instance crucial to define the desired equivariant maps).

[**Structure of the paper.**]{}  In Sect. 1, we define (simplicial and non-simplicial) Euclidean buildings and illustrate the notions in the case of the groups ${\rm SL}_n$; we also show in these cases how the natural group actions on the building encode information on the group structure of rational points. In Sect. 2, we illustrate general notions thanks to the examples of spaces naturally associated to special linear groups (such as projective spaces); this time the 