Muon Cooling is the key factor in building of a Muon collider, (to a less degree) Muon storage ring, and a Neutrino Factory. Muon colliders potential to provide a probe for fundamental particle physics is very interesting, but may take a considerable time to realize, as much more work and study is needed. Utilizing high intensity Muon sources - Neutrino Factories, and other intermediate steps are very important and will greatly expand our abilities and confidence in the credibility of high energy muon colliders. To obtain the needed collider luminosity, the phase-space volume must be greatly reduced within the muon life time. The Ionization cooling is the preferred method used to compress the phase space and reduce the emittance to obtain high luminosity muon beams. We note that, the ionization losses results not only in damping, but also heating. The use of alternating solenoid lattices has been proposed, where the emittance are large. We present an overview of the cooling and discuss formalism, solenoid magnets and some beam dynamics.
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