This article presents the physics case for a new high-energy, ultra-high statistics neutrino scattering experiment, NuSOnG (Neutrino Scattering on Glass). This experiment uses a Tevatron-based neutrino beam to obtain over an order of magnitude higher statistics than presently available for the purely weak processes $ u_{mu}+e^- to u_{mu}+ e^-$ and $ u_{mu}+ e^- to u_e + mu^-$. A sample of Deep Inelastic Scattering events which is over two orders of magnitude larger than past samples will also be obtained. As a result, NuSOnG will be unique among present and planned experiments for its ability to probe neutrino couplings to Beyond the Standard Model physics. Many Beyond Standard Model theories physics predict a rich hierarchy of TeV-scale new states that can correct neutrino cross-sections, through modifications of $Z u u$ couplings, tree-level exchanges of new particles such as $Z^prime$s, or through loop-level oblique corrections to gauge boson propagators. These corrections are generic in theories of extra dimensions, extended gauge symmetries, supersymmetry, and more. The sensitivity of NuSOnG to this new physics extends beyond 5 TeV mass scales. This article reviews these physics opportunities.
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