Aims.The goal of this work is to measure the evolution of the Galaxy Stellar Mass Function and of the resulting Stellar Mass Density up to redshift ≃4, in order to study the assembly of massive galaxies in the high redshift Universe. Methods: .We have used the GOODS-MUSIC catalog, containing 3000 Ks-selected galaxies with multi-wavelength coverage extending from the U band to the Spitzer 8 μm band, of which 27% have spectroscopic redshifts and the remaining fraction have accurate photometric redshifts. On this sample we have applied a standard fitting procedure to measure stellar masses. We compute the Galaxy Stellar Mass Function and the resulting Stellar Mass Density up to redshift ≃4, taking into proper account the biases and incompleteness effects. Results: .Within the well known trend of global decline of the Stellar Mass Density with redshift, we show that the decline of the more massive galaxies may be described by an exponential timescale of ≃6 Gyr up to z≃ 1.5, and proceeds mu
