Rotation and Mixing in Massive Stars: Principles and Uncertainties
  The main instabilities induced by rotation in stellar interiors are described. We derive from first principles the general equation describing the transport of the angular momentum. The case of the transport of the chemical species is also discussed. As long as the mass loss rates are not too important, meridional currents, by advecting angular momentum from the inner regions to the outer layers, accelerate the stellar surface during the Main Sequence phase. A 9 M$_\odot$ stellar model at solar metallicity with an equatorial velocity at the beginning of the core H--burning phase equal to 340 km s$^{-1}$ reaches the break--up limit during the MS phase. The model with an initial velocity of 290 km s$^{-1}$ approaches this limit without reaching it. The models with 290 km s$^{-1}$ and 340 km s$^{-1}$ predict enhancements of the N/C ratio at the end of the MS phase equal to 2.8 and 3.2 times the initial value respectively. 
Georges Meynet and Andre Maeder