Electronic Structure Reading Group: Green's functions in quantum many-body theory and quasiparticle equations

I am planning to give a general introduction about Green’s functions in quantum many-body theory and quasiparticle equation.
The main reference will be this paper of Behnam Farid:
Behnam Farid (1999) A Luttinger’s theorem revisited, Philosopical Magazine B, 79:8, 1097-1143, DOI: 10.1080/13642819908218309
Here I will just focus on sections 2 & 3 + Appendix A
Another good (but quite older) reference is in Layzer
https://journals.aps.org/pr/abstract/10.1103/PhysRev.129.897
Finally, and depending on time, I can show an example of application from this other paper of Engel and Farid et al.
https://journals.aps.org/prb/abstract/10.1103/PhysRevB.44.13356

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The electronic structure reading group brings together researchers and students interested in mathematical aspects of electronic structure problems and adjacent topics, including:

• Density Functional Theory
• Many-body Schrödinger equation for electrons
• Born-Oppenheimer Molecular Dynamics
• Numerical analysis and error control