This work is a sequel to the author's 'GoÌ?del's Incompleteness Theorems', though it can be read independently by anyone familiar with GoÌ?del's incompleteness theorem for Peano arithmetic. The text deals mainly with those aspects of recursion theory that have applications to the metamathematics of incompleteness, undecidability, and related topics. It is both an introduction to the theory and a presentation of new results in the field.