We present absorption line strength maps of 48 representative elliptical and lenticular galaxies obtained as part of a survey of nearby galaxies using our custom-built integral-field spectrograph, SAURON, operating on the William Herschel Telescope. Using high-quality spectra, spatially binned to a constant signal-to-noise ratio, we measure four key age, metallicity and abundance ratio sensitive indices from the Lick/IDS system over a two-dimensional field extending up to approximately one effective radius. A discussion of calibrations and offsets is given, along with a description of error estimation and nebular emission correction. We modify the classical Fe5270 index to define a new index, Fe5270S, which maximizes the useable spatial coverage of SAURON. Maps of Hβ, Fe5015, Mgb and Fe5270S are presented for each galaxy. We use the maps to compute average line strengths integrated over circular apertures of one-eighth effective radius, and compare the resulting relations of index versus velocity dispersion with previous long-slit work. The metal line strength maps show generally negative gradients with increasing radius roughly consistent with the morphology of the light profiles. Remarkable deviations from this general trend exist, particularly the Mgb isoindex contours appear to be flatter than the isophotes of the surface brightness for about 40 per cent of our galaxies without significant dust features. Generally, these galaxies exhibit significant rotation. We infer from this that the fast-rotating component features a higher metallicity and/or an increased Mg/Fe ratio as compared to the galaxy as a whole. The Hβ maps are typically flat or show a mild positive outwards radial gradient, while a few galaxies show strong central peaks and/or elevated overall Hβ strength likely connected to recent star formation activity. For the most prominent post-starburst galaxies, even the metal line strength maps show a reversed gradient.