  [Abridged] We analysed two-dimensional maps of 48 early-type galaxies
obtained with the SAURON and OASIS integral-field spectrographs using
kinemetry, a generalisation of surface photometry to the higher order moments
of the line-of-sight velocity distribution (LOSVD). In the SAURON sample, we
find that 31% of early-type galaxies are single component systems. 91% of the
multi-components systems have two kinematic subcomponents, the rest having
three. In addition, 29% of galaxies have kinematically decoupled components,
nuclear components with significant kinematic twists. We find that the velocity
maps of fast rotators closely resemble those of inclined disks, except in the
transition regions between kinematic subcomponents. In terms of E/S0
classification, this means that 74% of Es and 92% of S0s have components with
disk-like kinematics. For the majority of fast rotators, the kinematic axial
ratios are equal to or less than their photometric axial ratios, contrary to
what is predicted with isotropic Jeans models viewed at different inclinations.
The position angles of fast rotators are constant, while they vary abruptly in
slow rotators. Velocity dispersion maps of face-on galaxies have shapes similar
to the distribution of light. We constructed local (bin-by-bin) h3 - V/sigma
and h4 - V/sigma diagrams from SAURON observations. We confirm the classical
anti-correlation of h3 and V\sigma, but we also find that h3 is almost zero in
some objects or even weakly correlated with V/sigma. The distribution of h4 for
fast and slow rotators is mildly positive on average. The difference between
slow and fast rotators is traceable throughout all moments of the LOSVD, with
evidence for different intrinsic shapes and orbital contents and, hence, likely
different evolutionary paths.
