and [@RTW2]; it also contains some further developments which we found useful to mention here. The general theme is to explain what the theory of analytic spaces in the sense of Berkovich brings to the problem of compactifying Bruhat-Tits buildings.

[**1.**]{} [*Bruhat-Tits buildings*]{}.—  The general notion of a building was introduced by J. Tits in the 60ies [@TitsICM], [@Lie456 Exercises for IV.2]. These spaces are cell complexes, required to have some nice symmetry properties so that important classes of groups may act on them. More precisely, it turned out in practice that for various classes of algebraic groups and generalizations, a class of buildings is adapted in the sense that any group from such a class admits a very transitive action on a suitable building. The algebraic counterpart to the transitivity properties of the action is the possibility to derive some important structure properties for the group.

This approach is particularly fruitful when the class of groups is that of simple Lie groups over non-Archimedean fields, or more generally reductive groups over non-Archimedean valued fields – see Sect. \[s - Bruhat-Tits general\]. In this case the relevant class of buildings is that of Euclidean buildings (\[ss - Euclidean buildings\]). [*This 