The model calculations considered here test the DWBA with a wide range of three-body models. Each of the calculations, however, considers only one or two aspects of the accuracy of the DWBA. The lack of overlap of the testing parameters limits the con? clusions which can be drawn. This is particularly true with reference to the nucleon? core potential where comparable parameters are rarely used. In spite of this limitation, we may make a few observations about the sensitivity of the model cross sections and the mechanism which produces an accurate DWBA. Specifically we may summarize the most important results as follows: 1) In these models the exact DWBA at low energies (EWith contributions by numerous expertsThe model calculations considered here test the DWBA with a wide range of three-body models. Each of the calculations, however, considers only one or two aspects of the accuracy of the DWBA. The lack of overlap of the testing parameters limits the con? clusions which can be drawn. This is particularly true with reference to the nucleon? core potential where comparable parameters are rarely used. In spite of this limitation, we may make a few observations about the sensitivity of the model cross sections and the mechanism which produces an accurate DWBA. Specifically we may summarize the most important results as follows: 1) In these models the exact DWBA at low energies (E1. Fundamentals of Three-Body Scattering Theory.- 1.1 Two-Body Scattering.- 1.1.1 The Schr?dinger Equation.- 1.1.2 The Differential Cross Section.- 1.1.3 The Scattering Integral Equation.- 1.1.4 The Two-Body t-Matrix.- 1.1.5 The Separable Potential.- 1.2 The Simplest Three-Body Problem.- 1.2.1 Notation.- 1.2.2 The Two-Body t-Matrix in the Three-Body System.- 1.3 Three Distinguishable Particles Wave Function Approach.- 1.3.1 The Non-Uniqueness Problem.- 1.3.2 The Solution (3?3).- 1.3.3 Scattering from a Two-Body Bound State.- 1.4 The Faddeev Equations (3?3).- 1.4.1 A Rigorous Derivation of Fal#z