Beam cooling: principles and achievements

After a discussion of Liouvilleʹs theorem, and its implications for beam cooling, a brief description is given about each of the various methods of beam cooling: stochastic, electron, radiation, laser, ionization, etc. For each, we present the type of particle for which it is appropriate, its range of applicability, and the currently achieved degree of cooling. For each method, we also discuss the present applications and, also, possible future developments and further applications.