The goal of this project is to understand spin-dependent electron transmission and scattering in metallic multilayers composed of alternating magnetic and nonmagnetic materials. The experiments use successive magnetic layers as "polarizer" and "analyzer", with an external magnetic field controlling their relative orientation. Using a cryogenic scanning tunneling microscope, different spectroscopies detect either the ballistic electron current transmitted through the polarizer/analyzer pairs, or the field-dependent density of states in the multilayer. These are among the first detailed studies of spin-dependent scattering in metals and at subsurface interfaces for electron energies within +5 electron volt of the Fermi energy. They address issues of importance for understanding both the oscillatory exchange coupling and the giant magnetoresistance ratios that have been observed in magnetic multilayers. %%% This project addresses issues of importance for understanding the properties of "magnetic multilayers". These are thin films with alternating magnetic and nonmagnetic layers, each typically two nanometer thick. Because these man-made materials exhibit a "giant" magnetoresistance ratio, they have already found applications in ultrasmall and sensitive magnetic field sensors (in computer disk drives, for instance). Still, the fundamental basis for the observed magnetic effects is not fully understood. These experiments use the spectroscopic capabilities of a low- temperature scanning tunneling microscope to derive information about the properties of magnetic multilayers on a nanometer length scale. ***