A group of computational researchers of the University of Colorado-Denver will be involved in a study of multilevel algorithms, focussing on new technologies and advanced computational architerutres and environments. The research is categorized among the following eight topics: 1. Mixed Methods. 2. Iterative Refinement. 3. Highly Advective Flow. 4. Preconditioned Iterative Methods. 5. Multilevel Methods for Irregular Regions. 6. Multilevel Monte-Carlo. 7. Small-Scale Structural Singularities. 8. Quantitative Analysis.