Using a sample of ~28,000 sources selected at 3.6-4.5 microns with Spitzer observations of the HDF-N, the CDF-S, and the Lockman Hole (surveyed area: ~664 arcmin^2), we study the evolution of the stellar mass content of the Universe at 0<z<4. We calculate stellar masses and photometric redshifts, based on ~2,000 templates built with stellar and dust emission models fitting the UV-to-MIR SEDs of galaxies with spectroscopic redshifts. We estimate stellar mass functions for different redshift intervals. We find that 50% of the local stellar mass density was assembled at 0<z<1 (average SFR:0.048 M_sun/yr/Mpc^3), and at least another 40% at 1<z<4 (average SFR: 0.074 M_sun/yr/Mpc^3). Our results confirm and quantify the ``downsizing scenario of galaxy formation. The most massive galaxies (M>10^12.0 M_sun) assembled the bulk of their stellar content rapidly (in 1-2 Gyr) beyond z~3 in very intense star formation events (producing high specific SFRs). Galaxies with 10^11.5<M/M_sun<10^12.0 assembled half of their stellar mass before z~1.5, and more than 90% of their mass was already in place at z~0.6. Galaxies with M<10^11.5 M_sun evolved more slowly (presenting smaller specific SFRs), assembling half of their stellar mass below z~1. About 40% of the local stellar mass density of 10^9.0<M/M_sun<10^11.0 galaxies was assembled below z~0.4, most probably through accretion of small satellites producing little star formation. The cosmic stellar mass density at z>2.5 is dominated by optically faint (R>25) red galaxies (Distant Red Galaxies or BzK sources) which account for ~30% of the global population of galaxies, but contribute at least 60% to the cosmic stellar mass density. Bluer galaxies (e.g., Lyman Break Galaxies) are more numerous but less massive, contributing less than 50% to the global stellar mass density at high redshift.
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