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OvertureThe Universe as a set of harmonic oscillators Lagrangians Simple harmonic oscillators Occupation number representation Making second quantization workWriting down Lagrangians Continuous systems A first stab at relativistic quantum mechanics Examples of Lagrangians, or how to write down a theoryIII. The need for quantum fieldsThe passage of time Quantum mechanical transformations Symmetry Canonical quantization of fields Examples of canonical quantization Fields with many components and massive electromagnetism Gauge fields and gauge theory Discrete transformationsPropagators and perturbations Ways of doing quantum mechanics: propagators and Green’s functions Propagators and Fields The S-matrix Expanding the S-matrix: Feynman diagrams Scattering theoryInterlude: wisdom from statistical physics Statistical physics: a crash course The generating functional for fieldsPath Integrals Path Integrals: I said to him, “You’re crazy” Field Integrals Statistical field theory Broken symmetry Coherent states Grassmann numbers: coherent states and the path integral for fermionsVII. Topological ideasTopological objects Topological field theoryVIII. Renormalization: taming the infiniteRenormalization, quasiparticles and the Fermi surface Renormalization: the problem and its solution Renormalization in action: propagators and Feynman diagrams The renormalization group Ferromagnetism: a renormalization group tutorialPutting a spin on QFT The Dirac equation How to transform a spinor The quantum Dirac field A rough guide to quantum electrodynamics QED scattering: three famous cross sections The renormalization of QED and two great resultsSome applications from the world of condensed matter Superfluids The many-body problem and the metal Superconductors The fractional quantum Hall fluidSome applications from the world of particle physics Non-abelian gauge theory The Weinberg-Salam model Majorana fermions Magnetic monopoles Instantons, tunnelling and the end of the worldAppendix A. Further reading Appendix B. Useful complex analysis