Root systems and generalized associahedra

Contents Root systems and generalized associahedra 1 Root systems and generalized associahedra 3 Lecture 1. Reflections and roots 5 1.1. The pentagon recurrence 5 1.2. Reflection groups 6 1.3. Symmetries of regular polytopes 8 1.4. Root systems 11 1.5. Root systems of types A, B, C, and D 13 Lecture 2. Dynkin diagrams and Coxeter groups 15 2.1. Finite type classification 15 2.2. Coxeter groups 17 2.3. Other " finite type " classifications 18 2.4. Reduced words and permutohedra 20 2.5. Coxeter element and Coxeter number 22 Lecture 3. Associahedra and mutations 25 3.