  (Abridged) We present a stellar population analysis of the absorption line
strength maps for 48 early-type galaxies from the SAURON sample. Using the line
strength index maps of Hbeta, Fe5015, and Mgb, measured in the Lick/IDS system
and spatially binned to a constant signal-to-noise, together with predictions
from up-to-date stellar population models, we estimate the simple stellar
population-equivalent (SSP-equivalent) age, metallicity and abundance ratio
[alpha/Fe] over a two-dimensional field extending up to approximately one
effective radius. We find a large range of SSP-equivalent ages in our sample,
of which ~40% of the galaxies show signs of a contribution from a young stellar
population. The most extreme cases of post-starburst galaxies, with
SSP-equivalent ages of <=3 Gyr observed over the full field-of-view, and
sometimes even showing signs of residual star-formation, are restricted to low
mass systems(sigma_e <= 100 k/ms or ~2x10^10 M_sol). Spatially restricted cases
of young stellar populations in circumnuclear regions can almost exclusively be
linked to the presence of star-formation in a thin, dusty disk/ring, also seen
in the near-UV or mid-IR. The flattened components with disk-like kinematics
previously identified in all fast rotators (Krajnovi\'c et al.) are shown to be
connected to regions of distinct stellar populations. These range from the
young, still star-forming circumnuclear disks and rings with increased
metallicity preferentially found in intermediate-mass fast rotators, to
apparently old structures with extended disk-like kinematics, which are
observed to have an increased metallicity and mildly depressed [alpha/Fe] ratio
compared to the main body of the galaxy. The slow rotators generally show no
stellar population signatures over and above the well known metallicity
gradients and are largely consistent with old (>=10 Gyr) stellar populations.
