From the Preface to the First Edition (1906): "There are no definitely accepted landmarks in the didactic treatment of Georg Cantor's magnificent theory, which is the subject of the present volume. A few of the most modern books on the Theory of Functions devote some pages to the establishment of certain results belonging to our subject, and required for the special purposes in hand ... But we may fairly claim that the present work is the first attempt at a systematic exposition of the subject as a whole."

In this second edition, notes have been added by I. Grattan-Guinness drawn from extensive annotations in the author's own copy. A further appendix has been added.

Readership

Graduate students and research mathematicians.

Table of Contents

• Rational and irrational numbers
• Representation of numbers on the straight line
• The descriptive theory of linear sets of points
• Potency, and the generalised idea of a cardinal number
• Content
• Order
• Cantor's numbers
• Preliminary notions of plane sets
• Regions and sets of regions
• Curves
• Potency of plane sets
• Plane content and area
• Length and linear content
• Appendices
• Bibliography
• Index of proper names
• General index