The contributions that we have made during the grant period of DE-FG02-98ER45704 can be placed into six different categories: (1) advances in the Theory of Molecule-Surface Scattering, (2) advances in the Theory of Atom-Surface Scattering, (3) utilization of scattering theory to Extract Physical Information about Surfaces, (4) Gas-Surface Interactions, (5) Ion Scattering from surfaces and (6) Scanning Tunneling Microscopy (STM). These six topics are discussed below as individual listings under the title 'IV. Detailed description of research accomplishments'. These advances show that we have made significant progress on several scientific problems in atomic and molecular surface scattering during the course of this grant as well as contributions to other areas. It is also noted that this work, although fundamentally theoretical, is marked by its strong motivation to explain current experimental measurements. This was an important secondary goal in the proposed work. We have developed theory that is useful to experimentalists in the explanation and analysis of their experimental data.