Here is presented for the first time a comprehensive review and analysis of the several roles played by idealization procedures in the logic, mathematics and models that lie at the heart of modern, twentieth century physics. It is only through idealization of one form or another that the objects and processes of modern physics become tractable. The essays in this volume will be of interest to all those who are concerned with the uses of models in physics, and the relationships between models and the real world. The essays in this volume cover the role of idealization in all the main areas of modern physics, ranging from quantum theory, relativity theory and cosmology to chaos theory.