The oscillations of rapidly rotating stars

We review the effects of rotation on the oscillation spectrum of rapidly rotating stars. We particularly stress the novelties introduced by rotation: for instance, the disappearance of modes in the low frequency band due to the ill-posed natured of the underlying mathematical problem. This is mainly an effect of the Coriolis acceleration. The centrifugal effect changes the shape of the star in the first place. The possible consequences of this deformation on the oscillation spectrum are briefly analyzed. We also describe other possibly important effects of the centrifugal acceleration which come about on the time scale of star evolution.