Review of Nicolas Bouleau's book : Theory of errors.

Summary In 2003, Nicolas Bouleau published Error Calculus for Finance and Physics, The language of Dirichlet Forms, the fruit of two decades of research in the field of stochastic analysis and applied mathematics, with the objective of proposing a mathematically rigorous and operational approach to the handling of errors (in measurement or modeling) and their propagation. Published in the Nouvelle Bibliothèque Mathématique collection, this new book takes the challenge of making this fertile field of research accessible to a much wider public. This challenge is, in particular from a pedagogical point of view, amply successful. The reading of this book will satisfy both the undergraduate and graduate student, familiar with Differential Calculus and elementary probability theory, who wishes to apply his theoretical knowledge to applications, and the experienced modeler who wishes to develop a rigorous and critical engineering of his models. Finally, the researcher will find in this book material to think about the powerful Dirichlet theory of forms from an original angle. This book is composed of 5 parts with a strong emphasis on examples and applications.