1. Quick intro of example shape optimization problems. 2. Review differential geometry for curves/surfaces: parametric surfaces, normal vector, curvature, shape operator, etc. 3. Review surface differential operators: surface gradient/Laplacian, shape operator, integration by parts on surfaces, etc. 4. Intro shape perturbations: material and shape derivatives of functions, shape perturbation of shape functionals, perturbation of the identity, etc. 5. Intro gradient flows: motivate as a way to optimize shape, derive mean curvature flow. Maybe give example of image segmentation if there is time. 6. Application: work through a shape optimization problem with the Stokes equation as a PDE constraint.