A classic exposition of the branch of mathematical logic known as category theory, this text is suitable for advanced undergraduates and graduate students and accessible to both philosophically and mathematically oriented readers. Beginning with a survey of set theory and its role in mathematics, it proceeds to definitions and examples of categories and explains the use of arrows in the place of epsilon. Subsequent topics include topos logic, algebra of subobjects, intuitionism and its logic, functors, set concepts and validity, and elementary truth. Explorations of categorial set theory, local truth, and adjointness and quantifiers conclude with a study of logical geometry.