"Level Set Methods and Fast Marching Methods" by James A. Sethian is a comprehensive overview of the author's research on the theory and numerical methods for propagating interfaces. The book discusses two computational techniques: Fast Marching Methods and Level Set Methods, which are developed to model the evolution of boundaries. These methods are based on Eulerian initial value partial differential equations, which differ from traditional Lagrangian approaches. The book provides a mathematical theory of evolving boundaries and partial differential equations of motion, along with traditional methods for interface tracking and basic schemes for initial and boundary value problems. It also explains efficient schemes for interface motion computation and algorithm adaptivity. The second part of the book focuses on the application of these techniques in various fields, including geometry, grid generation, computer vision, combustion, solidification, fluid mechanics, and microchip fabrication. The book is divided into 22 chapters and is easy to read, making it a useful resource for mathematicians, applied scientists, engineers, and computer graphics artists. The second edition includes eight areas of possible applications and examples of the author's participation in these applications. The book serves as a framework for transforming new interface problems into partial differential equations. It has 378 pages and is published by Cambridge University Press."Level Set Methods and Fast Marching Methods" by James A. Sethian is a comprehensive overview of the author's research on the theory and numerical methods for propagating interfaces. The book discusses two computational techniques: Fast Marching Methods and Level Set Methods, which are developed to model the evolution of boundaries. These methods are based on Eulerian initial value partial differential equations, which differ from traditional Lagrangian approaches. The book provides a mathematical theory of evolving boundaries and partial differential equations of motion, along with traditional methods for interface tracking and basic schemes for initial and boundary value problems. It also explains efficient schemes for interface motion computation and algorithm adaptivity. The second part of the book focuses on the application of these techniques in various fields, including geometry, grid generation, computer vision, combustion, solidification, fluid mechanics, and microchip fabrication. The book is divided into 22 chapters and is easy to read, making it a useful resource for mathematicians, applied scientists, engineers, and computer graphics artists. The second edition includes eight areas of possible applications and examples of the author's participation in these applications. The book serves as a framework for transforming new interface problems into partial differential equations. It has 378 pages and is published by Cambridge University Press.