I: The Universe as a set of harmonic oscillators
1: Lagrangians
2: Simple harmonic oscillators
3: Occupation number representation
4: Making second quantization work
II: Writing down Lagrangians
5: Continuous systems
6: A first stab at relativistic quantum mechanics
7: Examples of Lagrangians, or how to write down a theory
III: The need for quantum fields
8: The passage of time
9: Quantum mechanical transformations
10: Symmetry
11: Canonical quantization of fields
12: Examples of canonical quantization
13: Fields with many components and massive electromagnetism
14: Gauge fields and gauge theory
15: Discrete transformations
IV: Propagators and perturbations
16: Ways of doing quantum mechanics: propagators and Green’s functions
17: Propagators and Fields
18: The S-matrix
19: Expanding the S-matrix: Feynman diagrams
20: Scattering theory
V: Interlude: wisdom from statistical physics
21: Statistical physics: a crash course
22: The generating functional for fields
VI: Path Integrals
23: Path Integrals: I said to him, “You’re crazy”
24: Field Integrals
25: Statistical field theory
26: Broken symmetry
27: Coherent states
28: Grassmann numbers: coherent states and the path integral for fermions
VII: Topological ideas
29: Topological objects
30: Topological field theory
VIII: Renormalization: taming the infinite
31: Renormalization, quasiparticles and the Fermi surface
32: Renormalization: the problem and its solution
33: Renormalization in action: propagators and Feynman diagrams
34: The renormalization group
35: Ferromagnetism: a renormalization group tutorial
IX: Putting a spin on QFT
36: The Dirac equation
37: How to transform a spinor
38: The quantum Dirac field
39: A rough guide to quantum electrodynamics
40: QED scattering: three famous cross sections
41: The renormalization of QED and two great results
X: Some applications from the world of condensed matter
42: Superfluids
43: The many-body problem and the metal
44: Superconductors
45: The fractional quantum Hall fluid
XI: Some applications from the world of particle physics
46: Non-abelian gauge theory
47: The Weinberg-Salam model
48: Majorana fermions
49: Magnetic monopoles
50: Instantons, tunnelling and the end of the world
Appendix A: Further reading
Appendix B: Useful complex analysis