Points and lines in the plane --Circles and spheres --The sphere by itself: can we distribute points on it evenly? --Conics and quadrics --Plane curves --Smooth surfaces --Convexity and convex sets --Polygons, polyhedra, polytopes --Lattices, packings and tilings in the plane --Lattices and packings in higher dimensions --Geometry and dynamics I: billiards --Geometry and dynamics II: geodesic flow on a surface.