am 14. Juni 2014
In my opinion, this book fills a gap.
The problem when you want to start learning QFT and do not attend, for instance because you specialize in a more experimental section, a lecture, you find yourself being overwhelmed by the amount of literature available on the subject. The level of sophistication of the sevearl textbooks differs - a good starting point is in my eyes still Griffiths: Introduction to Elementary Particle Physics, which enables you to bulge through some cross-section calculations and model f.i. massive photons in the exercises. Afterwards, stuff like Aitchinson Hey should have become accessible to read, and ponder exercisewisely. However, both texts could provide the image of QFT being only applied in particle physics, which is certainly not true. In fact, several applications from condensed matter physics aid more pedagogically for understanding stuff better - renormalization group methods are in my eyes better explained in statistical physics than directly in quantum field theory. Also, some of the condensed matter physics applications were more graspable to me in the first place - but this of course highly subjective.
Furthermore, other books usually proceed traditionally via the canonical quantization approach. This is pedagogically in order, but the path integral approach gives you handy methods for calculating and devising some cool models.
In fact, the book is in principle what it claims to be - quantum field theory, and not only (not to be misunderstood as pejorative) QFT merged with particle physics.
About the contents of the book itself. I particularly like the inclusion of a "wisdom from statistical physics" part, for reasons that I have given before. Secondly, the short, but very clear treatise on QFT for spin-1/2's with a photon field (QED) is very nicely written - and not too long! Personally, I have always found that the calculation of cross sections, and only QED stuff is not so motivational for students like me. Rather, giving directly path-integral methods and actually showing the applicability of QFT not only in the form of QED is very helpful.
The later sections, for instance the treatments of YM-theory, Instantons, Dirac-Monopoles in the realm of particle physics is thin - but I consider this to some extent as an advantage because, unless you are specializing in theoretical particle physics for instance, you would not be in need for all the technicalities that occur there. The person interested in some of the more technical details (in particle physics) can for instance consult Schwartz' QFT book, which I prefer above Peskin a bit. For Condesend Matter applications, the classic reference is the Altland-book. If you want to enjoy some equation checking and quickly proceed to String theory and stuff the traditional way (leanign towards concepts, not so mich calculations), I'd recommend to you Kaku's QFT (beware of typos), who contains some interesting exercises (not every one, but yeah).
As for the mathematical background, I would, anyway support comforting yourself with Hassani-books, or, if you are german-speaking, the Goldstein or Fischer-Kaul series is also very helpful. To get a feeling what the guys from mathe-department prove all-day-long, you can read and do some of the exercises of Storch-Wiebes 4-volume tome (~3500pp.) "Lehrbuch der Mathematik". You could deepen your understanding especially of topology by consulting Nakhara, Frankel (I only partially recommend this book) or, my favorite, Bo-Yuan, which should, nonetheless be read after Nakahara.
The lack of solutions to problems is quite normal, and I would to some extent consider it not necessarily as a problem. In general, I use more than one book for learning a subject, and sometimes, some of the more difficult exercises can be found in other books worked out as part of the theory.
Sometimes, even knowing that solutions to exercises, proofs to theorems exist can have its own value.