(in no specific order. The topics are tentative and may be adjusted along the way.)
Shape representations in computer graphics: parametric surfaces, implicit surfaces, point-based surfaces, polygonal meshes and subdivision surfaces.
Related data structures: spatial partitioning, mesh data structures.
Shape acquisition and reconstruction. More on implicit representations, Moving Least Squares, Marching Cubes.
Linear algebra tools for geometric modeling: spectral decompositions (connection to DCT and mesh compression), PCA and SVD (normal estimations, local shape matching).
Differential geometry primer: tangents and normals, fundamental forms, curvatures and (discrete) differential operators.
Digital geometry processing: resampling, parameterization, smoothing, remeshing and compression.
Mesh deformation intro. Surface-based methods vs. space deformations.
Differential surface editing techniques. Poisson and Laplacian mesh editing, advanced nonlinear techniques.
Optimization methods used for shape processing and manipulation. Least squares, direct solvers, iterative methods, nonlinear solvers.
Space deformation techniques: classic FFD, radial basis functions, cage-based approaches.
Sketch-based interfaces for shape creation and editing. Teddy, FiberMesh, SilSketch.
More applications of geometric optimizations: skinning and animation