Is mathematics free of contradictions? Are there truths beyond what can be proven? Is it possible to encode our mathematical knowledge into a single number? The modern mathematical logic of the twentieth century provides astonishing answers to such questions. This book takes you on a journey through the core areas of mathematical logic, exploring the boundaries of mathematics. Among other topics, it covers: the history of mathematical logic, formal systems, axiomatic number theory and set theory, proof theory, Gödel's incompleteness theorems, computability theory, algorithmic information theory, and model theory. The book includes numerous two-color illustrations and more than 70 exercises (with solutions available on the book's website). For the third edition, the chapter on 'Model Theory' has been expanded to include a description of the work by Pa.