A muon collider is expected to produce a high intensity neutrino beam which is an admixture of either $ν_μ+\bar{ν_e}$ or $\barν_μ +ν_e$ which can can be directed to underground detectors far away from the source. It will not only allow a probe of the $ν_e-ν_μ$ as well as $ν_μ-ν_τ$ oscillations in a range of mixing angle and $Δm^2$ not probed heretofore but it will also provide information about the mixing angle $θ_{eτ}$ for a wide range of $Δm^2_{ν_eν_τ}$ from $10^{-4}$ eV$^2$ to $10^{-1}$ eV$^2$ which cannot be obtained from any other existing or proposed machine. One can also search for violations of Lorentz invariance and deviations from equivalence principle for neutrinos at a level which is three to four orders of magnitude more sensitive than possible at the moment. This will test for instance some unorthodox suggestions to understand both solar and atmospheric neutrinos using a single mass difference -squared between the $ν_e$ and $ν_μ$. It can also test various proposed models neutrino masses and mixings to understand existing neutrino data.

Some parts of the text changed; major conclusions unchanged