Structural Proof Theory is a branch of logic that studies the general structure and properties of logical and mathematical proofs. This book is both a concise introduction to the central results and methods of structural proof theory and a work of research that will be of interest to specialists. The book is designed to be used by students of philosophy, mathematics, and computer science. The book contains a wealth of new results on proof-theoretical systems, including extensions of such systems from logic to mathematics, and on the connection between the two main forms of structural proof theory natural deduction and sequent calculus. The authors emphasize the computational content of logical results. A special feature of the volume is a computerized system for developing proofs interactively, downloadable from the web and regularly updated.