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1. Introduction 2. Perturbative quantum field theory 3. The Hopf algebra structure of renormalization 4. Rationality: no knots, no transcendentals 5. The simplest link diagrams 6. Necessary topics from knot theory 7. Knots to numbers 8. One-loop words 9. Euler-Zagier sums 10. Knots and transcendentals 11. The 4-term relation 12. Hopf algebras, non-commutative geometry, and what else?