Context : Large grids of synthetic spectra covering a widespread range of stellar parameters are mandatory for different stellar and ( extra- ) Galactic physics applications .
For instance , such large grids can be used for the automatic parametrisation of stellar spectra such as that performed within the AMBRE project for which the main goal is the stellar atmospheric parameters determination for the few hundreds of thousands of archived spectra of four ESO spectrographs .

Aims : To fulfil the needs of AMBRE and future similar projects , we have computed a grid of synthetic spectra over the whole optical domain for cool to very cool stars of any luminosity ( from dwarfs to supergiants ) with metallicities varying from 10 ^ { -5 } to 10 times the solar metallicity , and considering large variations in the chemical content of the \alpha -elements .

Methods : For these spectrum computations , new generation MARCS model atmospheres and the Turbospectrum code for radiative transfer have been used .
We have also taken into account as complete as possible atomic and molecular linelists and adopted , in the spectral synthesis , the same physical assumptions and input data as in the MARCS models .
This allowed us to present a grid with a high consistency between the atmosphere models and the synthetic spectra .

Results : A new grid of 16 783 high resolution spectra over the wavelength range 3 000 to 12 000 Å has been computed with a spectral resolution always larger than 150 000 .
Normalised and absolute flux versions are available over a wide range of stellar atmospheric parameters for stars of FGKM spectral types .
The covered parameters are 2 500 K \leq T _ { eff } \leq 8 000 K , -0.5 \leq log ( g ) \leq 5.5 dex and -5.0 \leq [ M/H ] \leq +1.0 dex .
Moreover , for each combination of these stellar parameters , five different values of the enrichment in \alpha -elements have been considered ( 0.0 , \pm 0.2 dex and \pm 0.4 dex around the standard values ) .
This library is thus relevant for any stellar type and luminosity class , present in old and intermediate-age stellar populations from extremely metal-poor to metal-rich in content .
This grid is made publicly available through the POLLUX database ( about 50 % of the spectra are already included in this database ) and in FITS format upon request to the authors .

Conclusions :