We present the stellar kinematics of 48 representative elliptical and lenticular galaxies obtained with our custom-built integral-field spectrograph SAURON operating on the William Herschel Telescope. The data were homogeneously processed through a dedicated reduction and analysis pipeline. All resulting SAURON datacubes were spatially binned to a constant minimum signal-to-noise. We have measured the stellar kinematics with an optimized (penalized pixel-fitting) routine which fits the spectra in pixel space, via the use of optimal templates, and prevents the presence of emission lines to affect the measurements. We have thus generated maps of the mean stellar velocity, the velocity dispersion, and the Gauss-Hermite moments h3 and h4 of the line-of-sight velocity distributions. The maps extend to approximately one effective radius. Many objects display kinematic twists, kinematically decoupled components, central stellar disks, and other peculiarities, the nature of which will be discussed in future papers of this series.
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