The evolution of rotating stars

In this article we first review the main physical effects to be considered in the building of evolutionary models of rotating stars on the Upper Main-Sequence (MS). The internal rotation law evolves as a result of contraction and expansion, meridional circulation, diffusion processes, and mass loss. In turn, differential rotation and mixing exert a feedback on circulation and diffusion, so that a consistent treatment is necessary. We review recent results on the evolution of internal rotation and the surface rotational velocities for stars on the Upper MS, for red giants, supergiants, and W-R stars. A fast rotation enhances the mass loss by stellar winds and, conversely, high mass loss removes a lot of angular momentum. The problem of the breakup or Omega -limit is critically examined in connection with the origin of Be and LBV stars. The effects of rotation on the tracks in the HR diagram, the lifetimes, the isochrones, the blue-to-red supergiant ratios, the formation of Wolf-Rayet stars, and the chemical abundances in massive stars as well as in red giants and AGE stars are reviewed in relation to recent observations for stars in the Galaxy and Magellanic Clouds. The effects of rotation on the final stages and on the chemical yields are examined, along with the constraints placed by the periods of pulsars. On the whole, this review points out that stellar evolution is not only a function of mass M and metallicity Z, but of angular velocity Omega as well.