The modeling of interfacial motion is an essential task in many problems in science and engineering. One class of methods is capturing methods, in which the interface is implicitly embedded in a scalar field function defined on a fixed mesh, such as a Cartesian grid. The interface dynamics are captured by the evolution of the scalar function in an Eulerian framework. The main advantages of capturing methods are (1) a geometric problem is turned into a partial differential equation problem on a fixed grid with simple data structure, (2) topological changes, such as merging or splitting, can be handled easily in the viscosity sense. In this course, students will concentrate on the level set method and study both the theoretical and numerical aspects of the algorithm. Students should seek the course instructor’s approval to take this course.