This book, "Numerical Methods for Conservation Laws" by Randall J. LeVeque, is a comprehensive text on the numerical solution of conservation laws, particularly for nonlinear systems involving shock waves. It is based on a course taught at the University of Washington and ETH Zürich. The book emphasizes the mathematical tools essential for developing, analyzing, and using numerical methods for conservation laws. It begins with an overview of conservation laws, their applications, and the mathematical and numerical challenges involved. The first part of the book covers the theory of conservation laws, including scalar conservation laws, shock formation, and entropy conditions. The second part focuses on numerical methods, discussing general tools and underlying ideas rather than detailed algorithms. The author aims to provide a solid foundation for students to engage with current research literature. The book includes detailed discussions on various numerical methods, such as Godunov's method, approximate Riemann solvers, and high-resolution methods. It also addresses issues like numerical stability, accuracy, and the treatment of discontinuities. The text is supported by a bibliography and is intended to be a resource for both students and researchers in the field of numerical methods for conservation laws. The author encourages feedback and suggestions for future improvements. The book is published by Springer Basel AG and was originally published by Birkhäuser Verlag. It is written in English and is suitable for advanced undergraduate and graduate students in mathematics and related fields.This book, "Numerical Methods for Conservation Laws" by Randall J. LeVeque, is a comprehensive text on the numerical solution of conservation laws, particularly for nonlinear systems involving shock waves. It is based on a course taught at the University of Washington and ETH Zürich. The book emphasizes the mathematical tools essential for developing, analyzing, and using numerical methods for conservation laws. It begins with an overview of conservation laws, their applications, and the mathematical and numerical challenges involved. The first part of the book covers the theory of conservation laws, including scalar conservation laws, shock formation, and entropy conditions. The second part focuses on numerical methods, discussing general tools and underlying ideas rather than detailed algorithms. The author aims to provide a solid foundation for students to engage with current research literature. The book includes detailed discussions on various numerical methods, such as Godunov's method, approximate Riemann solvers, and high-resolution methods. It also addresses issues like numerical stability, accuracy, and the treatment of discontinuities. The text is supported by a bibliography and is intended to be a resource for both students and researchers in the field of numerical methods for conservation laws. The author encourages feedback and suggestions for future improvements. The book is published by Springer Basel AG and was originally published by Birkhäuser Verlag. It is written in English and is suitable for advanced undergraduate and graduate students in mathematics and related fields.