Volume one of this two volume sequence focuses on the basic characterization of known protein structures as well as structure prediction from protein sequence information. The 11 chapters provide an overview of the field, covering key topics in modeling, force fields, classification, computational methods, and struture prediction. Each chapter is a self contained review designed to cover (1) definition of the problem and an historical perspective, (2) mathematical or computational formulation of the problem, (3) computational methods and algorithms, (4) performance results, (5) existing software packages, and (6) strengths, pitfalls, challenges, and future research directions.