  We present deep long-slit optical spectra for a sample of 36 Ultraluminous
Infrared Galaxies (ULIRGs), taken with the William Herschel Telescope (WHT) on
La Palma with the aim of investigating the star formation histories and testing
evolutionary scenarios for such objects. Here we present the sample, the
analysis techniques and a general overview of the properties of the stellar
populations. Spectral synthesis modelling has been used in order to estimate
the ages of the stellar populations found in the diffuse light sampled by the
spectra in both the nuclear and extended regions of the target galaxies. We
find that adequate fits can be obtained using combinations of young stellar
populations (YSPs,t_YSP<=2 Gyr), with ages divided into two groups: very young
stellar populations (VYSPs, t_VYSP <=100 Myr) and intermediate-young stellar
populations (IYSPs, 0.1 < t_IYSP <= 2 Gyr). Our results show that YSPs are
present at all locations of the galaxies covered by our slit positions, with
the exception of the northern nuclear region of the ULIRG IRAS 23327+2913.
Furthermore, VYSPs are presents in at least 85% of the 133 extraction apertures
used for this study. Old stellar populations (OSPs, t_{OSP} > 2 Gyr) do not
make a major contribution to the optical light in the majority of the apertures
extracted. In fact they are essential for fitting the spectra in only 5% (7) of
the extracted apertures. The estimated total masses for the YSPs (VYSPs+IYSPs)
are in the range 0.18 x 10^{10} <= M_YSP <= 50 x 10^{10} Msun. We have also
estimated the bolometric luminosities associated with the stellar populations
detected at optical wavelengths, finding that they fall in the range 0.07 x
10^{12} < L_bol < 2.2 x 10^{12} Lsun. In addition, we find that reddening is
significant at all locations in the galaxies.
