I have a research project involving ultrametric spaces, and there are some facts that I use but have a hard time finding explicitely in the literature, although I know that some of them are folklore (for example, an ultrametric space can be described as the set of leaves of a tree, endowed with the induced metric).
I would like to know whether there is a book or comprehensive survey paper on the geometry and structure of ultrametric spaces.
An important point: I am interested in purely metric spaces, without algebraic structure (I did find books on analysis in non-Archimedean fields, which are too focused on this case). I can restrict to compact spaces, but not to finite ones.