This two-volume work bridges the gap between introductory expositions of logic or set theory on one hand and the research literature on the other. It can be used as a text in an advanced undergraduate or beginning graduate course in mathematics computer science or philosophy. The volumes are written in a user-friendly conversational lecture style that makes them equally effective for self-study or class use. Volume 1 includes formal proof techniques a section on applications of compactness (including nonstandard analysis) a generous dose of computability and its relation to the incompleteness phenomenon and the first presentation of a complete proof of Godel's 2nd incompleteness since Hilbert and Bernay's Grundlagen theorem. Language: English