  We study galaxy evolution from z=1 to z=0 as a function of velocity
dispersion sigma for galaxies with sigma > 95 km/s based on the measured and
Monte Carlo realised local velocity dispersion functions (VDFs) of galaxies and
the revised statistical properties of 30 strongly-lensed sources. We assume
that the total (luminous plus dark) mass profile of a galaxy is isothermal in
the optical region for 0 < z < 1 as suggested by mass modelling of lensing
galaxies. For the evolutionary behaviours of the VDFs we find that: (1) the
number density of massive (mostly early-type) galaxies with sigma > 200 km/s
evolves differentially in the way that the number density evolution is greater
at a higher velocity dispersion; (2) the number density of intermediate and low
mass early-type galaxies (95 km/s < sigma < 200 km/s) is nearly constant; (3)
the late-type VDF transformed from the Monte Carlo realised circular velocity
function is consistent with no evolution in its shape or integrated number
density consistent with galaxy survey results. These evolutionary behaviours of
the VDFs are strikingly similar to those of the dark halo mass function (DMF)
from N-body simulations and the stellar mass function (SMF) predicted by recent
semi-analytic models of galaxy formation under the current LambdaCDM
hierarchical structure formation paradigm. Interestingly, the VDF evolutions
appear to be qualitatively different from ``stellar mass-downsizing''
evolutions obtained by many galaxy surveys. The coevolution of the DMF, the VDF
and the SMF is investigated in quantitative detail in a following paper. We
consider several possible systematic errors for the lensing analysis and find
that they are not likely to alter the conclusions.(abridged)
