This goal of this research is to develop an understanding of the fundamental nature of giant magnetoresistance (GMR) displayed in periodic multilayers and single layer alloy thin films. The main effort is on optimizing GMR in cobalt-silver multilayers and co- sputtered alloy films. The multilayer variables include layer thickness, layer number, buffer layer materials, and annealing heat treatment. Co-sputtered film variables include the cobalt/silver concentrations and sputtering pressure. Effects of third elemental additions are to be determined. Structure, magnetoresistance, and general magnetic properties are measured using a variety of techniques. Also emphasized is computer simulation of the GMR behavior using a Monte Carlo approach to microstructural evolution. %%% This research on magnetoresistance in thin films and multilayers is pertinent to the development of magnetic field sensors, such as read heads in magnetic recording technology.