The paper presents a fast marching level set method for monotonically advancing fronts, which is an efficient scheme for solving the Eikonal equation. Level set methods are numerical techniques that use an initial value partial differential equation for a propagating level set function to track the evolution of interfaces. The method is particularly useful for problems involving topological changes, corner and cusp development, and accurate geometric properties such as curvature and normal direction. The technique combines entropy conditions for interface motion, viscosity solutions for Hamilton–Jacobi equations, and fast adaptive narrow band level set methods. It is applicable to various problems, including shape-from-shading, lithographic development, and arrival time problems in control theory. The paper details the algorithm, provides a proof of its correctness, and discusses its efficiency and applications. The method is demonstrated through examples such as lithographic development and isotropic deposition, showing its effectiveness and speed.The paper presents a fast marching level set method for monotonically advancing fronts, which is an efficient scheme for solving the Eikonal equation. Level set methods are numerical techniques that use an initial value partial differential equation for a propagating level set function to track the evolution of interfaces. The method is particularly useful for problems involving topological changes, corner and cusp development, and accurate geometric properties such as curvature and normal direction. The technique combines entropy conditions for interface motion, viscosity solutions for Hamilton–Jacobi equations, and fast adaptive narrow band level set methods. It is applicable to various problems, including shape-from-shading, lithographic development, and arrival time problems in control theory. The paper details the algorithm, provides a proof of its correctness, and discusses its efficiency and applications. The method is demonstrated through examples such as lithographic development and isotropic deposition, showing its effectiveness and speed.