  Wide-field JHKs near-infrared observations covering an area of 1.8x1.8 sq.
deg. centred on M33 were obtained using WFCAM at UKIRT. These data show a large
population of intermediate-age asymptotic giant branch stars (AGB). We have
used both C-type and M-type AGB stars to determine spatial variations in
metallicity and mean age across the galaxy. We distinguished between C-type and
M-type AGB stars from their location in the colour-magnitude diagram (J-Ks,
Ks). The distribution of these stars is supported by a cross-identification
between our sample and a catalogue of optically confirmed, long-period variable
stars, as well as with the list of sources detected by Spitzer in the
mid-infrared. We calculated the C/M ratio and the orientation of the galaxy in
the sky, and compared the Ks magnitude distribution with theoretical
distributions spanning a range of metallicities and star formation rates
(SFRs). The C/M ratio surface map confirms a metallicity gradient in the galaxy
corresponding to a spread in [Fe/H]=0.6 dex with substructures in the inner and
outer galaxy. Magnitude and colour variations suggest orientation and
extinction effects on the galaxy disc. Maps showing the distribution of mean
age and metallicity obtained from the Ks method suggest that: the outer galaxy
disc/halo is metal poorer than the nuclear region and metal-rich clumps in the
inner galaxy change location with time. The average outer ring and nuclear
stellar population is ~6 Gyr old while central regions are a few Gyr younger.
