Not a book, but Terence Tao's blog had very frequently clarified my understanding and giving me insight that I did not have. As an example, I was thoroughly confused with analytic number theory, like the prime number theorem, but music note analogy and the self-defeating conspiracy argument from Tao's blog make it so intuitive.

The blog also cover a wide range of topic. Sure he's an analyst, but that does not mean he can't cover other topics, with his own perspective.