  We present a detailed analysis of the Galaxy Stellar Mass Function of
galaxies up to z=2.5 as obtained from the VVDS. We estimate the stellar mass
from broad-band photometry using 2 different assumptions on the galaxy star
formation history and show that the addition of secondary bursts to a
continuous star formation history produces systematically higher (up to 40%)
stellar masses. At low redshift (z=0.2) we find a substantial population of
low-mass galaxies (<10^9 Msun) composed by faint blue galaxies (M_I-M_K=0.3).
In general the stellar mass function evolves slowly up to z=0.9 and more
significantly above this redshift. Conversely, a massive tail is present up to
z=2.5 and have extremely red colours (M_I-M_K=0.7-0.8). We find a decline with
redshift of the overall number density of galaxies for all masses (59+-5% for
M>10^8 Msun at z=1), and a mild mass-dependent average evolution
(`mass-downsizing'). In particular our data are consistent with mild/negligible
(<30%) evolution up to z=0.7 for massive galaxies (>6x10^10 Msun). For less
massive systems the no-evolution scenario is excluded. A large fraction (>=50%)
of massive galaxies have been already assembled and converted most of their gas
into stars at z=1, ruling out the `dry mergers' as the major mechanism of their
assembly history below z=1. This fraction decreases to 33% at z=2. Low-mass
systems have decreased continuously in number and mass density (by a factor up
to 4) from the present age to z=2, consistently with a prolonged mass assembly
also at z<1.
