  Given a non-trivial complete valued field $K$ with value group $\Lambda$, we
construct a $\Lambda$-tree space associated to $K$ analog of the Bruhat-Tits
tree, and locally finite trees associated to compact subsets of the projective
line. We propose a definition of hyperbolic matrix and Schottky group over such
field $K$. To any such Schottky group $\Gamma$, we associate a compact set with
an action of $\Gamma$, such that the quotient graph of the associated tree is a
finite graph, and $\Gamma$ is identified with its fundamental group. Finally
explain a method to construct such groups. This results extend the classical
ones for discrete valuations of Mumford and non-archimedean rank 1 valuations
of Gerritzen and Van der Put.
