  We investigate the evolution of the galaxy luminosity function from the
VIMOS-VLT Deep Survey (VVDS) from the present to z=2 in five (U, B, V, R and I)
rest-frame band-passes. We use the first epoch VVDS deep sample of 11,034
spectra selected at 17.5 <= I_{AB} <= 24.0, on which we apply the Algorithm for
Luminosity Function (ALF), described in this paper. We observe a substantial
evolution with redshift of the global luminosity functions in all bands. From
z=0.05 to z=2, we measure a brightening of the characteristic magnitude M*
included in the magnitude range 1.8-2.5, 1.7-2.4, 1.2-1.9, 1.1-1.8 and 1.0-1.6
in the U, B, V, R and I rest-frame bands, respectively. We confirm this
differential evolution of the luminosity function with rest-frame wavelength,
from the measurement of the comoving density of bright galaxies (M <
M*(z=0.1)). This density increases by a factor of around 2.6, 2.2, 1.8, 1.5,
1.5 between z=0.05 and z=1 in the U, B, V, R, I bands, respectively. We also
measure a possible steepening of the faint-end slope of the luminosity
functions, with \Delta\alpha ~ -0.3 between z=0.05 and z=1, similar in all
bands.
