The book "Level Set Methods and Fast Marching Methods" by James A. Sethian, published by Cambridge University Press in its second edition in June 1999, provides an overview of the author's work on the theory and numerics of propagating interfaces. Propagating interfaces are prevalent in various natural and artificial phenomena, such as ocean waves, burning flames, crystal growth, handwritten characters, and iso-intensity contours in images. The book is divided into two parts: the first part covers the mathematical theory, including the partial differential equations of motion, traditional methods for interface tracking, and basic schemes for initial and boundary value problems. The second part focuses on applications of both Fast Marching Methods and Level Set Methods in various fields, such as geometry, grid generation, computer vision, combustion, solidification, fluid mechanics, and microchip fabrication. The book offers a robust framework for modeling the evolution of boundaries and is accessible to mathematicians, applied scientists, engineers, and computer graphics artists.The book "Level Set Methods and Fast Marching Methods" by James A. Sethian, published by Cambridge University Press in its second edition in June 1999, provides an overview of the author's work on the theory and numerics of propagating interfaces. Propagating interfaces are prevalent in various natural and artificial phenomena, such as ocean waves, burning flames, crystal growth, handwritten characters, and iso-intensity contours in images. The book is divided into two parts: the first part covers the mathematical theory, including the partial differential equations of motion, traditional methods for interface tracking, and basic schemes for initial and boundary value problems. The second part focuses on applications of both Fast Marching Methods and Level Set Methods in various fields, such as geometry, grid generation, computer vision, combustion, solidification, fluid mechanics, and microchip fabrication. The book offers a robust framework for modeling the evolution of boundaries and is accessible to mathematicians, applied scientists, engineers, and computer graphics artists.