. CW-pumped polarization-maintaining Brillouin fiber ring laser: I. Self-structuration of Brillouin solitons. Optics Communications, Elsevier, 2006, 257, pp.319-333. 10 Abstract Stimulated Brillouin scattering (SBS) of a cw-pump in a low optical fiber ring cavity generates for a given gain G -below a critical feedback R crit -a backward soliton Stokes pulse at the roundtrip repetition rate, through resonant three-wave interaction between the optical pump wave and backward Stokes wave, and a high frequency (GHz) axial acoustic wave. In Part I, we perform a systematic experimental and numerical exploration of the whole soliton localisation domain for a large set of (G, R) parameters, in a polarization-maintaining Brillouin fiber ring laser in the best conditions of stability and coherence, and we confirm the excellent quantitative agreement of the coherent three-wave model and the experiments.