Lecture 1. From billiards to flat surfaces
Lecture 2. Magic Wand Theorem
Lecture 3. Ramified covers. Cyclic covers. Holonomy. Monodromy. Intersection number
Lecture 4. Idea of Renormaliation
Lecture 5. (by Bram Petri) Integration on moduli spaces
Lecture 6. Mirzakhani's count of simple closed geodesics
Lecture 7. Train tracks. Measured laminations. Proof of Mirzakhani's count
Lecture 8. Count of flat closed geodesics. Siegel–Veech formula
Lecture 9. Masur–Veech volumes and square–tiled surfaces
Lecture 10. Masur–Veech volumes and Witten–Kontsevich correlators. Random square-tiled surfaces and random multicurves
Suggestions for reading before bed