Set theory, initially built on the Cantorian extension of number into the infinite and the Zermelian axiomatization affirming a foundation for mathematics, is today a rich and sophisticated field of mathematics which, having been invested with model-building techniques of Goedel

and Cohen, incorporates into its ongoing investigation of infinite sets a full range of strong hypotheses involving large cardinalities.

This volume serves as a companion to set theory, in that it gathers together essays that illuminate the historical development, philosophical resonances, and current mathematical activity. Part I, History, has essays on the development and involvements of set theory in the early 20th Century, essays that bring out the interplay with then ongoing mathematics. Part II, Philosophy, has essays that take up related issues and considerations in the philosophy of mathematics and its practice. Part III, Mathematics, has a few mathematical papers of modern set theory that with their thematic reach qualify them as essays''. Finally, Part IV, Lives in Set Theory, has essays on the life work of prominent set theorists to the present day, essays that exhibit mathematical research.