Implicit surfaces: Implicit functions ; Signed distance functions -- Level set methods: Motion in an externally generated velocity field ; Motion involving mean curvature ; Hamilton-Jacobi equations ; Motion in the normal direction ; Constructing signed distance functions ; Extrapolation in the normal direction ; Particle level set methods ; Codimension-two objects -- Image processing and computer vision: Image restoration ; Snakes, active contours, and segmentation ; Reconstruction of surfaces from unorganized data points -- Computational physics: Hyperbolic conservation laws and compressible flow ; Two-phase compressible flow ; Shocks, detonations, and deflagrations ; Solid-fluid coupling ; Incompressible flow ; Free surfaces ; Liquid-gas interactions ; Two-phase incompressible flow ; Low-speed flames ; Heat flow