This timely work is the first book in several years to review and update important developments in the study of rings of continuous functions. Integrating the recent efforts of leading mathematicians, Rings of Continuous Functions presents chapters with varying emphasis on algebra, analysis, and general topology with particular focus on category theory, cardinality axioms, and set theory. Additionally, historical perspectives and a review of early contributions by leading Soviet mathematicians such as P. S. Aleksandrov and A. N. Tychonov help provide a full, up-to-date understanding of current knowledge. An unparalleled overview of the state of the art, Rings of Continuous Functions will be an invaluable reference for topologists, algebraists, analysts, and geometers active in the field, and an excellent introduction for interested nonspecialist mathematicians. Also, research problems raised in each chapter and in a special final chapter offer provocative avenues for further research -- facilitated by more than 300 literature citations. Book jacket.