  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.
