Increasing interest in set theory, particularly the possibility of a set of all sets ("universal set"), has been stimulated by its relevance to computer science. This new edition, drawing heavily on Quine's theories as introduced in New Foundations , provides an accessible introduction of universal set theory to mathematicians, logicians, and philosophers. Included are expanded accounts of the set theories of Church, Oswald and Mitchell, with descriptions of permutation models and extensions that preserve power "...a lively introduction to the current research..."-- Modern Logic "The best survey of its field available, with an excellent bibliography."-- Journal of Symbolic Logic This book is an essay: not a monograph, or a textbook, but an essay. It is intended to be a good read for those people who are already interested in this topic (or think they might be interested in it) rather than a comprehensive treatment for people who wish to master it, and a reference work for people who already have. T. E. Forster is at University of Cambridge.