Abstract : This project concerns the design and analysis of algorithms to be run in a processor-rich environment. We focus primarily on algorithms that require no global control and that can be run on systems with only local connections among processors. We investigate the properties of these algorithms both theoretically and experimentally. The experimental work is done on the ZMOB, a working parallel computer operated by the Laboratory for Parallel Computation of the Computer Science Department at the University of Maryland. To give our work direction, we have focused on two areas: 1. Dense problems from numerical linear algebra; and 2. The iterative and direct solution of sparse linear systems. We discuss in this summary the ZMOB hardware and the research projects that we have pursued under this grant support.