The broad aim of this work is to understand the molecular forces that determine the interaction of proteins with ligands. The goal is the development of the theory needed for molecular design. This project focuses on computer-assisted design of ligands for macromolecular receptors of known structure using a program called DOCK. The DOCK program creates negative images of receptor surfaces and positive images of ligands. It then explores in a systematic way the six degrees of freedom involved in fitting together two rigid bodies. It does this operation rapidly enough that we can use a large structural database - the Cambridge Crystallographic Database -- as a source of steric molecular templates for ligand design. In the coming grant period we need 1) to automate the procedure of adding polar atoms to the templates, 2) to improve the basic algorithms used in DOCK for control of the search procedure, 3) to develop a better user interface and 4) to explore new databases. We also want to follow up some new applications of the mathematics, such as the study of the packing of macromolecules. This approach to ligand design has had some very recent initial successes in the development of novel lead compounds as inhibitors of the HIV protease. There is some hope that it will form the basis of a powerful structural-based effort to speed up the entire drug design process.