A noted logician and philosopher addresses various forms of mathematical logic, discussing both theoretical underpinnings and practical applications. Author Hao Wang surveys the central concepts and theories of the discipline in a historical and developmental context, and then focuses on the four principal domains of contemporary mathematical logic: set theory, model theory, recursion theory and constructivism, and proof theory. Topics include the place of problems in the development of theories of logic and logic's relation to computer science. Specific attention is given to Gödel's incompleteness theorems, predicate logic and its decision and reduction problems, constructibility and Cantor's continuum hypothesis, proof theory and Hilbert's program, hierarchies and unification, proof of the four-color problem, the Diophantine problem, the tautology problem, and many other subjects. Three helpful Appendixes conclude the text.