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I am looking for a self-contained book that explains the concepts of QFT in the most general way but that still explains the mathematical concepts which surprass the general level of physics undergraduate studies. Also, it should describe the full Standard Model of particle physics with method of QFT. Does anyone have some recomendations?

Qmechanic
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I know at least two great book for what you need. This is very popular: "An Introduction To Quantum Field Theory" by Michael Peskin and Daniel Schroeder. The second one is "Field Quantization" by Walter Greiner.

I think this two will do it, since it contains all the concepts behind QFT, in a very nice structure.

Have fun!