Abstract-This paper presents a novel geometric approach for learning and reproducing trajectory-based skills from human demonstrations. Our approach models a skill as a Generalized Cylinder, a geometric representation composed of an arbitrary space curve called spine and a smoothly varying cross-section. While this model has been utilized to solve other robotics problems, this is the first application of Generalized Cylinders to manipulation. The strengths of our approach are the model's ability to identify and extract the implicit characteristics of the demonstrated skill, support for reproduction of multiple trajectories that maintain those characteristics, generalization to new situations through nonrigid registration, and interactive human refinement of the resulting model through kinesthetic teaching. We validate our approach through several real-world experiments with a Jaco 6-DOF robotic arm.