  The aim of the talk is to trace how and when Henri Poincar\'e used
non-Euclidean geometries (NEG) in his mathematical and philosophical works,
with a particular attention to the genesis and the description of his model. We
begin by a short presentation of the context of NEG in France around the
1870-80s. Then we expound from several sources the introduction and use of NEG
in Poincar\'e's work about Fuchsian functions and we stress on the analogy
between elliptic functions and fuchsian functions.
