1. Introduction
1.1. Motivation
1.2. Photons, waves and fields
1.3. A necessary note
part I. Basic photon states. 2. Field quantisation
2.1. Quantum mechanical background
2.2. Harmonic oscillator
2.3. Electromagnetic field quantisation
2.4. Canonical quantisation
2.5. Photon wavefunction
2.6. Quantisation in a medium
3. Coherence
3.1. Coherent states
3.2. Field representations
3.3. Squeezed states
3.4. Correlations
3.5. Photon entanglement
4. Photon-atom interactions
4.1. Hamiltonians
4.2. Quantum Rabi model
4.3. Three-level atom
4.4. Spontaneous emission
4.5. Reduced density method
4.6. Resonant scattering
5. Boundary effects
5.1. Cavity losses
5.2. Atom in a cavity
5.3. Beam splitters
5.4. Time refraction
5.5. Temporal beam splitters
5.6. Time-crystals
5.7. Casimir force
5.8. Space-time symmetries
5.9. Curved space-time
part II. Quantum fluids of light. 6. Laser
6.1. Balance equations
6.2. Laser cavity
6.3. Phenomenological laser model
6.4. Relaxation oscillations
6.5. Short laser pulses
6.6. Amplified spontaneous emission
6.7. Susceptibility
6.8. Semi-classical laser theory
6.9. Quantum laser theory
7. Bose-Einstein condensates
7.1. Basic concepts
7.2. Photon condensation
7.3. Condensation in plasma
7.4. Polariton condensation
7.5. BEC-laser transition
7.6. Photon kinetics
8. Collective atomic emission
8.1. Superradiance
8.2. Collective recoil emission
8.3. Quantum recoil
8.4. Cyclotron superradiance
9. Light vortices
9.1. Photon OAM
9.2. Light springs and fractional vorticity
9.3. POAM in optical media
9.4. Quantum optics with OAM
10. Superfluid light
10.1. Fluid equations of light
10.2. Superfluid turbulence
10.3. A tale of two fluids
10.4. Superfluid currents
part III. Quantum vacuum. 11. Basic QED concepts
11.1. Klein-Gordon equation
11.2. Dirac equation
11.3. Volkov states
11.4. Quantisation of the Dirac field
11.5. Euler-Heisenberg Lagrangian
12. Particle pair creation
12.1. Klein paradox
12.2. Temporal Klein model
12.3. Time-varying fields
12.4. Nonlinear trident process
13. Nonlinear vacuum
13.1. Vacuum birefringence
13.2. Photon acceleration
13.3. Photon-photon scattering
13.4. Vacuum undulator
13.5. Superradiant vacuum
14. The axions
14.1. Axion-photon coupling
14.2. Axion polariton
14.3. Axion beam instability
14.4. Axion wakes
14.5. Shinning through wall
Appendix A. Elementary quantum
Appendix B. Lagrangians
Appendix C. Photon kinetic equation
Appendix D. Curved spacetime.