I try to read Godel's Proof once a year or so. You might also be interested in Gregory Chaitin's Meta Math! The Quest For Omega, which relates the halting probl

I try to read Godel's Proof once a year or so. You might also be interested in Gregory Chaitin's Meta Math! The Quest For Omega, which relates the halting problem (among other things) to Godel. A word of warning though, the book is rather idiosyncratic, as you might have seen from the title.