Computability and logic - Boolos, George (Cambridge University Press, 2002)
Now in its fourth edition, this book has become a classic because of its accessibility to students without a mathematical background, and because it covers not only the staple topics of an intermediate logic course such as Godel's Incompleteness Theorems, but also a large number of optional topics from Turing's theory of computability to Ramsey's theorem. John Burgess has enhanced the book by adding a selection of problems at the end of each chapter