2011 Reprint of 1960 Edition. Full facsimile of the original edition, not reproduced with Optical Recognition Software. Paul Richard Halmos 1916-2006 was a Hungarian-born American mathematician who made fundamental advances in the areas of probability theory, statistics, operator theory, ergodic theory, and functional analysis in particular, Hilbert spaces. He was also recognized as a great mathematical expositor. ...He the author uses the language and notation of ordinary informal mathematics to state the basic set-theoretic facts which a beginning student of advanced mathematics needs to know...Because of the informal method of presentation, the book is eminently suited for use as a textbook or for self-study. The reader should derive from this volume a maximum of understanding of the theorems of set theory and of their basic importance in the study of mathematics. - Philosophy and Phenomenological Research.