If you are mathematically-inclined and are looking forward to understanding the proof itself, the book won't do much better than the following video [1] taken from a comment in this thread [2]. Disappointed, I attempted to read Godel's original papers. That has it's own challenge as it refers to Principia Mathematica. I started reading that. Only to fimd that it uses older mathematical notation not in use today.

In short, I haven't found any source that explains the proof in reasonable detail.

If you want to understand the thought process of axiomatic reasoning (and with less extrapolations to consciousness et al) it is a good book.

Note: I had read a long time back, so do not remember the details.

[1] https://www.youtube.com/watch?v=HeQX2HjkcNo

[2] https://news.ycombinator.com/user?id=littlecranky67