• 1: Introduction
• 2: Graphs, maps and polynomials
• 3: Quantum field theory (QFT)
• 4: Tree weights and renormalization in QFT
• 5: Combinatorial QFT and the Jacobian Conjecture
• 6: Fermionic QFT, Grassmann calculus and combinatorics
• 7: Analytic combinatorics and QFT
• 8: Algebraic combinatorics and QFT
• 9: QFT on the non-commutative Moyal space and combinatorics
• 10: Quantum gravity, Group Field Theory and combinatorics
• 11: From random matrices to random tensors
• 12: Random tensor models - the U(N)D-invariant model
• 13: Random tensor models - the multi-orientable (MO) model
• 14: Random tensor models - the O(N)3 invariant model
• 15: The Sachdev-Ye-Kitaev holographic model
• 16: SYK-like tensor models
• Appendix
• A: Examples of tree weights
• B: Renormalization of the Grosse-Wulkenhaar model, one-loop examples
• C: The B+ operator in Moyal QFT, two-loop examples
• D: Explicit examples of GFT tensor Feynman integral computations
• E: Coherent states of SU(2)
• F: Proof of the double scaling limit of the U(N)D??invariant tensor model
• G: Proof of Theorem 15.3.2
• H: Proof of Theorem 16.1.1
• J: Summary of results on the diagrammatics of the coloured SYK model and of the Gurau-Witten model
• Bibliography