  Context: Extremely metal-poor stars (EMP) are very rare objects that hold in
their atmospheres the fossil record of the chemical composition of the early
phases of Galactic evolution. Finding these objects and determining their
chemical composition provides important constraints on these early phases.
Aims: Using a carefully designed selection method, we chose a sample of
candidate EMP stars from the low resolution spectra of the Sloan Digital Sky
Survey and observed them with X-Shooter at the VLT to confirm their
metallicities and determine abundances for as many elements as possible.
Method: The X-Shooter spectra are analysed by means of one-dimensional,
plane-parallel, hydrostatic model atmospheres. Corrections for the granulation
effects are computed using CO5BOLD hydrodynamical simulations. Results: All the
candidates are confirmed to be EMP stars, proving the efficiency of our
selection method within about 0.5 dex. The chemical composition of this sample
is compatible with those of brighter samples, suggesting that the stars in the
Galactic halo are well mixed. Conclusions These observations show that it is
feasible to observe, in a limited amount of time, a large sample of about one
hundred stars among EMP candidates selected from the SDSS. Such a size of
sample will allow us, in particular, to confirm or refute the existence of a
vertical drop in the Galactic Halo metallicity distribution function around
[Fe/H] ~ -3.5.
