Self-teaching Green's function approach to quantum many-body systems My question is where can I find a good book, review, online course, or all of them for self-teaching Green's function in quantum many-body problems (if it has problems with solutions for self-evaluating the concepts the better).
As I start to dig in the field, I find very nice books on one-particle green's function (e.g. Economou's book). However, the many-body non-equilibrium Green's function is presented always in a cloud of mysticism understandable only for people in field.
I am acquaintance with one particle Green's function at Sakurai's (scattering) level, but no more than that.
 A: There are many resources on many-body Green's functions (propagators) both on-line and in print. You may want to search "quantum field methods in many-particle systems" or "quantum field methods for condensed matter systems" or variations thereof. 
In any case, I personally recommend the oldie-but-goodie book by Fetter and Walecka, Quantum Theory of Many-Particle Systems. It assumes a good footing in Quantum Theory and Statistical Mechanics, but otherwise covers everything you need for a good handle on the field's basic methods, starting with second quantization and up to finite-temperature and real-time Green's functions. It also includes problems. A Dover edition on Amazon sells for about $21 (new), but I found an on-line copy here:
Fetter and Walecka, Quantum Theory of Many-Particle Systems
Other books available on-line, last one I didn't use directly, but all cover the basics in good detail:
H.Kleinert, Path Integrals in Quantum Mechanics, Statistics, Polymer Physics, and Financial Markets. Chap.2 covers the Field Formulation of Many-Body Quantum Physics pretty thoroughly, good intro.
Through the Mueller Group course site at Cornell, Basic Training in Condensed Matter Physics/Many Body Field Theory (unfortunately it seems it is no longer properly maintained since not all links check out anymore; listing only the two working ones for intro material): 
Brouwer, Theory of Many-Particle Systems
Nayak, Quantum Condensed Matter Physics
Also check their good list of in-print resources.
A: I highly recommend Richard D. Mattuck A Guide to Feynman Diagrams in the Many-Body Problem. You can read some pages here.
It's a very surface level introduction, but the first 3 or so chapters are presented at what he calls a "kindergarten" level so you shouldn't have any problems understanding it. However, the last part is most definitely not "kindergarten". 
