A two-day workshop was held on August 5 and 6, 1976, to discuss phase space damping (''cooling'') of particle beams. Two cooling techniques have been developed: in stochastic cooling the spread of amplitudes in a beam is reduced by a feedback signal derived from the statistical fluctuations in the beam; in electron cooling an electron beam having the same mean velocity as the heavy particle (proton or antiproton) beam coincides with the heavy beam in part of the orbit. Viewed in the center-of-mass system, the electrons are ''cold'' and the protons ''hot'', and in the approach to thermal equilibrium the protons are cooled down; in the lab system this means their fluctuations from the mean are reduced. Both these cooling techniques are discussed, especially with a view to their application to the production of intense high-quality antiproton beams suitable for colliding beam physics.