A complete understanding of any biological system or disease necessitates a detailed analysis of how its proteins interact with other molecules. Most methods for predicting and understanding protein function have focused on determining evolutionary relationships in amino acid sequences. However, the molecular function of a protein is determined also by its 3D structure (i.e., how atoms interact within its active sites), and thus a great deal of attention has recently been devoted towards solving the 3D structures of proteins with the hope that computer algorithms can infer functional relationships between them. 3D atomic coordinates are available for tens of thousands of proteins and the number has been increasing exponentially over the last several years. The goal of this project is to develop novel computer algorithms for analyzing protein structures, detecting similarities between them, visualizing how they interact with other molecules, and automatically providing functional classifications for them. For example, given a novel protein structure, new geometric algorithms will be used to determine the locations and shapes of its active sites. Next, the model of the structural and chemical properties of those sites will be used to search large databases for sites with similarities. Finally, the best matches are aligned so that functional annotations can be transferred from the active site of one protein to another. These algorithms will not only be useful for molecular biology, but they will drive research on a broader class of computation methods for detecting features in noisy 3D data, matching shapes of complex 3D structures, and searching large repositories of 3D data. Beyond the research, the project will have impact through its interdisciplinary collaborations, educational and outreach programs, and public dissemination of information. The project is a collaborative effort across diverse disciplines, aiding the project to promote cross-pollination of ideas between fields, and provide new educational opportunities for students to learn in an inter-disciplinary environment. Everything developed as part of this proposal will be made freely available to the public through talks, workshops, web pages, course notes, software libraries, bibliographies, and data sets.