This thoroughly revised second edition of a classic book on the main ideas and results of general meta-mathematics contains new results and simplified proofs, as well as an up to date bibliography. In addition to the standard results of Gödel and others on incompleteness, (non) finite axiomatizability, interpretability, etc.., it contains a thorough treatment of partial conservativity and degrees of interpretability. The reader should be familiar with the widely used method of arithmetization and with the elements of recursion theory.