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In this thesis we study the (inverse) back-scattering problem for the Schr"odinger operator in $R^3$. We introduce the back-scattering transform $B(v)$ of a real-valued potential $vin C_0^infty(R^3)$, and prove that the back-scattering data associated to $v$ determine $B(v)$. Under the assumption that the Schr"odinger operator $H_v=-Delta +v$ has no eigenvectors in $L^2(R^3)$ it is shown that $B(v
