It was published in 1958 by Państwowe Wydawnictwo Naukowe, as volume 34 of the series Monografie Matematyczne of the Institute of Mathematics of the Polish Academy of Sciences.

[1][2] Sierpiński wrote on the same topic earlier, in his 1928 book Leçons sur les nombres transfinis, but his 1958 book on the topic was completely rewritten and significantly longer.

[1][2] The second edition makes only minor changes to the first except for adding footnotes concerning two later developments in the area: the proof by Paul Cohen of the independence of the continuum hypothesis, and the construction by Robert M. Solovay of the Solovay model in which all sets of real numbers are Lebesgue measurable.

[2] Sierpiński was known for his significant contributions to the theory of transfinite numbers;[1][3], reviewer Reuben Goodstein calls his book "a goldmine of results",[3] and similarly Leonard Gillman writes that it is highly valuable "as a compendium of interesting mathematical information, presented with care and clarity".

Both Gillman and John C. Oxtoby call the writing style "leisurely" and "unhurried",[1][2] and although Gillman criticizes the translation from an earlier Polish-language manuscript into English as unpolished, and points to several errors in the bibliography, he does not find the writing in the text of the book to be problematic.