The Hubble constant (H0) value is subject to a tension at 5 sigma level between the estimate obtained through the cosmic ladder and that inferred from the early universe based on the Plank satellite measurements.

Classical Cepheids (DCEPs) are the key standard candles of the cosmic distance scale. The main aim of the C-MetaLL project is to establish the metallicity dependence of DCEP period-luminosity (PL) relations and to investigate its impact on the estimate of H0 through the cosmic ladder method. To this aim, we will measure the metallicity through high-resolution spectroscopy and will get multiband photometry, including in JHKs bands, for a sample of 350 Galactic DCEPs, greatly enlarging the parameter space for the PLs determination with respect to the literature.