  We describe the observing strategy, data reduction tools and early results of
a supernova (SN) search project, named SUDARE, conducted with the ESO VST
telescope aimed at measuring the rate of the different types of SNe in the
redshift range 0.2<z<0.8. The search was performed in two of the best-studied
extragalactic fields, CDFS and COSMOS, for which a wealth of ancillary data are
available in the literature or public archives.
  (abridged)
  We obtained a final sample of 117 SNe, most of which are SNIa (57%) and the
remaining core collapse events of which 44% type II, 22% type IIn and 34% type
Ib/c. In order to link the transients, we built a catalog of ~1.3x10^5 galaxies
in the redshift range 0<z<1 with a limiting magnitude K_AB=23.5 mag. We
measured the SN rate per unit volume for SN Ia and core collapse SNe in
different bin of redshifts. The values are consistent with other measurements
from the literature. The dispersion of the rate measurements for SNe Ia is
comparable with the scatter of the theoretical tracks for single (SD) and
double degenerate (DD) binary systems models, therefore the data do not allow
to disentangle among the two different progenitor scenarios. However, we may
notice that among the three tested models, SD and two flavours of DD, either
with a steep (DDC) or a wide (DDW) delay time distribution, the SD gives a
better fit across the whole redshift range whereas the DDC better matches the
steep rise up to redshift ~1.2. The DDW appears instead less favoured. The core
collapse SN rate is fully consistent, unlike recent claims, with the prediction
based on recent estimates of the star formation history, and standard
progenitor mass range.
