It is generally accepted that the afterglow is produced when the relativistic ejecta is slowed down by the surrounding matter . The afterglow begins at Rext where most of the energy of the ejecta is transferred to the shocked external medium. For a long burst this takes place while the burst is still going on (see Sari  and Section VID). Initially the process might be radiative, namely a significant fraction of the kinetic energy is dissipated and the radiation process effects the hydrodynamics of the shock. I discuss this phase in Section VIIC. Later the radiation processes become less efficient and an adiabatic phase begins during which the radiation losses are minor and do not influence the hydrodynamics. The hydrodynamic evolution at this stage is adiabatic. If the ejecta is in the form of a jet with an opening angle then a jet transition will take place when reaches -1. A transition into the Newtonian regime takes place when - 1 0.5. I begin the discussion of the afterglow with the hydrodynamics of the adiabatic phase and with the resulting synchrotron light curve. I continue with a discussion of the possible early radiative evolution. Then I turn to the jet break and to the Newtonian transition. I continue with various complications and variations on these themes.