A No-Nonsense Introduction to Quantum Field Theory

Veltman's book Diagrammatica is awesome when it comes to the basics of field theory and what it all means.

Reading through that one is in my opinion getting it right from the horse's mouth. Not heavy on the calculations but more on how the QFT and it's tools all work together to form a coherent picture of the subject.

It's true that it's a 300 page book, but I think you'll find that it's really easy to read. It's not high powered math and honestly I haven't found anything that got to the heart of the matter as quickly or with less math. QFT is a big subject and GR is more standalone. Reading a chapter in that book will run you about 20 min and it doesn't hurt the brain because it's all stuff an undergrad can easily do. The other reviews of QFT I've seen are very technical and extremely dense. Let me know if you find a better shorter alternative: I'd like to read something that succinct myself!

Gerard 't Hooft's "Quantum Field Theory for Elementary Particles. Is Quantum Field Theory a theory?" (Phys. Rept. 104 nos. 2-4 (1984), 129-142, author's eprint) is a beautifully written review. From the abstract,

What I would like to point out is that renormalizability is just one step in an evolutionary process of quantum field theory. In order to illuminate this point of view I will present a survey of the evolution of quantum field theory into its present form. However we will not follow the historical development, but rather, for my convenience, the lines of logic. As is well known, that is quite something different.

't Hooft also has a longer introduction to the subject:

The conceptual basis of Quantum Field Theory. Gerard 't Hooft. In Philosophy of Physics (J. Butterfield & J. Earman, eds., Elsevier/North-Holland: Amsterdam, 2007). Author's eprint.

This reads more like a textbook geared at readers with fairly solid quantum mechanics and a good understanding of special relativity, and covers a rather wide range of topics, so it is a little more advanced.

There is a great introduction called "This is How Quantum Field Theory Works" which, I think, is exactly what you are looking for.

All essential concepts are introduced and the basic idea how one gets from the fundamental equations to cross sections, i.e. quantities that can be measured in experiments is sketched.