This book specifically explores the inverse Schrödinger scattering problem in three dimensions with a potential that is without any assumed symmetry properties. It covers most of the known methods for the exact solution of this problem, including detailed proofs of most of the needed theorems. The solutions of the three-dimensional inverse-scattering problem found during the last twenty years are presented together for the first time in coherent, self-contained, and detailed manner. This book combines the known results published previously in research papers only, corrects some errors, closes some blind alleys in previous developments, and also contains a number of new results.