This book, "Numerical Methods for Conservation Laws" by Randall J. LeVeque, is a comprehensive guide to the numerical solution of conservation laws, originally published in 1992 and reprinted by Springer Basel AG. The author, Randall J. LeVeque, emphasizes the importance of understanding the mathematical structure of these equations and their solutions, particularly for problems involving shock waves. The book is divided into two main parts: Part I covers the mathematical theory, including the derivation of conservation laws, scalar and nonlinear systems, and the Riemann problem. Part II focuses on numerical methods, discussing various techniques such as upwind methods, Godunov's method, approximate Riemann solvers, and high-resolution methods. The book aims to provide a solid foundation for students to approach current research literature and includes a detailed bibliography. LeVeque acknowledges the support of Jürgen Moser and Martin Gutknecht, and expresses his gratitude to the National Science Foundation for partial funding.This book, "Numerical Methods for Conservation Laws" by Randall J. LeVeque, is a comprehensive guide to the numerical solution of conservation laws, originally published in 1992 and reprinted by Springer Basel AG. The author, Randall J. LeVeque, emphasizes the importance of understanding the mathematical structure of these equations and their solutions, particularly for problems involving shock waves. The book is divided into two main parts: Part I covers the mathematical theory, including the derivation of conservation laws, scalar and nonlinear systems, and the Riemann problem. Part II focuses on numerical methods, discussing various techniques such as upwind methods, Godunov's method, approximate Riemann solvers, and high-resolution methods. The book aims to provide a solid foundation for students to approach current research literature and includes a detailed bibliography. LeVeque acknowledges the support of Jürgen Moser and Martin Gutknecht, and expresses his gratitude to the National Science Foundation for partial funding.