This course was an exploration in the modern view of Geometry. Starting with Euclidean, the framework introduced is used throughout the semester.Then we studied Affine and Projective through lectures, and either Hyperbolic or Spherical via a final project. By far the most interesting course I've taken, but if proofs are not your strong suit this will be difficult. As an upper level course, proofs are the focus, every theorem in a lecture is proven so ensure you grasp the process (you don't need to memorize all the details though). The fundamental language of the course is linear algebra, so ensure you are strong in that area. Weekly problem sets are on average moderate in difficulty if you understand the material, but if there are gaps in your understanding it is exponentially more difficult. There were two take home midterms and one final project, and as long as you're good in the homework you're chilling for the midterms. However, writing up the final project was a long process and its dates overlap with preparation for the second midterm so the last 2 weeks were intense. Filippo is passionate and knows the material as well as the back of his hand, and is also a pretty generous grader. Interesting course on a beautiful subject.