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When I ask questions on this site regarding Feynman diagram, I see a lot of answers using functional method in QFT (e.g. this post and this post).

However, they seems quite confusing to me because I've only read Peskin & Schroeder's book in QFT. They do cover the functional method in chapter 9 but information on chapter 9 seems to be not detailed enough for me to understand post like this.

I am wondering if there's any recommended materials to supplement P&S's book on the functional methods of QFT (e.g. lecture notes, books). It would be great if the recommendation includes user-friendly materials and materials with detailed derivation.I am specifically interested in methods associated with generating functionals.

Interstellar
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By far my favourite text for the more advanced parts of QFT (including 1PI diagrams and effective actions) is Schwartz's Quantum Field Theory and The Standard Model. It's treatment is practical and physical due to its emphasis on calculations and link to experiments. But, unlike P&S I find it has a much more modern view on QFT and effective field theories.

Some very detailed and free notes with a modern viewpoint are the notes of David Skinner (which first discusses 1PI diagrams in the context of zero-dimensional QFT on page 32 of the chapter QFT in Zero Dimensions). I must admit I have not read much of these myself but I took a similar course which had the same overall approach just with a smaller amount of mathematical detail than he goes into in these notes. From what I have read, the approach is fairly mathematical so it depends a bit on taste whether these are for you (one approach could be to focus on the parts about practical calculation to begin with and only worry about the intricacies of the mathematics on a second reading). The nice part about these is that he introduces the high-power machinery of functional integrals and effective actions in a zero dimensional QFT to start off. This makes it much easier to see whats happening at the core without the concepts getting lost in the large amount of mathematical manipulations that come with higher dimensions. The notes technically assume you have already taken a first course in QFT (canonical quantisation, quantum electrodynamics etc) though you could get away without the first course if you are prepared to spend a bit my time with them (path integrals are really an alternative formalism to canonical quantisation and emphatically not an extension of it so, there is no real sense in which path intergrals must "come after" canonical quantisation).

Nic Christopher
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