  We present the first results of the Multi-Instrument Kinematic Survey of
Galactic Globular Clusters, a project aimed at exploring the internal
kinematics of a representative sample of Galactic globular clusters from the
radial velocity of individual stars, covering the entire radial extension of
each system. This is achieved by exploiting the formidable combination of
multi-object and integral field unit spectroscopic facilities of the ESO Very
Large Telescope. As a first step, here we discuss the results obtained for 11
clusters from high and medium resolution spectra acquired through a combination
of FLAMES and KMOS observations. We provide the first kinematical
characterization of NGC 1261 and NGC 6496. In all the surveyed systems, the
velocity dispersion profile declines at increasing radii, in agreement with the
expectation from the King model that best fits the density/luminosity profile.
In the majority of the surveyed systems we find evidence of rotation within a
few half-mass radii from the center. These results are in general overall
agreement with the predictions of recent theoretical studies, suggesting that
the detected signals could be the relic of significant internal rotation set at
the epoch of the cluster's formation.
