Set theory is that branch of mathematics in which the classical or platonist conception receives its fullest mathematical expression. It also has a foundational character, providing at least one general setting for most other matical theories. The work of Georg Cantor, the nineteenth-century founder of set theory, is for these reasons universally acknowledged as of fundamental importance. Michael Hallett's book is the first full-length study of Cantor that does justice both to the mathematical importance of his work and to the philosophical ideas which governed it. Cantor's own writings lay much stress upon the philosophical views which, for him, were indispensable to an understanding of the significance of his work and of the justification for the manner in which he carried it out. Hitherto, these philosophical ideas have been neglected by philosophers and mathematicians alike.