Abstract
In this thesis work, full Stokes (I, Q, U et V) spectropolarimetric observations of cool evolved stars have been analysed.I have measured a weak magnetic field at the surface of three well known red supergiant stars. Furthermore, I have shown that the strong level of linear polarisation, measured for these stars, can lead to some ambiguity in the measurement of magnetic fields. This strong, unmagnetic, linear polarisation originate from depolarisation of the continuum which, in turn, is only detectable because of symmetry-breaking effects on the stellar disk. I study in some details the continuum polarisation of RSG stars and I present a way of mapping symmetry-breaking strucutres through the mean of a spectropolarimetric model. Good agreement with interferometric observations is reached. From their side, pulsating variable stars also show strong linearly polarised features in their spectra. These features are indeed due to resonant scattering polarisation associated to metallic lines, a phenomenon reminiscent of the second solar spectrum. For these stars, the velocity gradients, pertaining to the shock waves propagating through their atmosphere, enhance the intrinsic polarisation of the lines. This Doppler brightening effect, well known in the solar case, offer a new innovative method for the analysis of these stars.