For those who want more details about Turing Machines and the Halting Problem, including a look at Turing's original paper, my usual advice is to read "The Annotated Turing" by Charles Petzold [ http://theannotatedturing.com/ ].

Here's a review of the book by the Notices of the AMS [ http://www.ams.org/notices/201108/rtx110801120p.pdf ]