  Rotation plays a key role in stellar structure and its evolution. Through
transport processes which induce rotational mixing of chemical species and the
redistribution of angular momentum, internal stellar rotation influences the
evolutionary tracks in the Hertzsprung-Russell diagram. In turn, evolution
influences the rotational properties. Therefore, information on the rotational
properties of the deep interior would help to better understand the stellar
evolution. However, as the internal rotational profile cannot be measured
directly, it remains a major unknown leaving this important aspect of models
unconstrained. We can test for nonrigid rotation inside the stars with
asteroseismology. Through the effect of rotational splitting of non-radial
oscillation modes, we investigate the internal rotation profile indirectly. Red
giants have very slow rotation rates leading to a rotational splitting on the
level of a few tenth of a \mu Hz. Only from more than 1.5 years of consecutive
data from the NASA Kepler space telescope, these tiny variations could be
resolved. A qualitative comparison to theoretical models allowed constraining
the core-to-surface rotation rate for some of these evolved stars. In this
paper, we report on the first results of a large sample study of splitting of
individual dipole modes.
