  Context. M subdwarfs are metal poor and cool stars. They are important probes
of the old galactic populations. However, they remain elusive due to their low
luminosity. Observational and modeling efforts are required to fully understand
their physics and to investigate the effects of metallicity in their cool
atmospheres.
  Aims. We perform a detailed study of a sample of subdwarfs to determine their
stellar parameters and constrain the stat-of-the art atmospheric models.
  Methods. We present UVES/VLT high resolution spectra of three late-K
subdwarfs and 18 M subdwarfs. Our atlas covers the optical region from 6400 AA
up to the near infrared at 8900 AA. We show spectral details of cool
atmospheres at very high resolution (R= 40 000) and compare with synthetic
spectra computed from the recent BT-Settl atmosphere models.
  Results. Our comparison shows that molecular features (TiO, VO, CaH), and
atomic features (Fe I, Ti I, Na I, K I) are well fitted by current models. We
produce an effective temperature versus spectral type relation all over the
subdwarf spectral sequence. Thanks to the high resolution of our spectra, we
perform a detailed comparison of line profiles of individual elements such as
Fe I, Ca II, Ti I, and are able to determine accurate metallicities of these
stars. These determinations contribute to calibrate the relation between
metallicity and molecular band strength indices from low-resolution spectra.
  Conclusions. This work shows that the new generation of models are able to
reproduce various spectral features of M subdwarfs. Working with these high
resolution spectra allowed us to disentangle the atmospheric parameters
(effective temperature, gravity, metallicity), which is not possible when using
low resolution spectroscopy or photometry.
