"An admirable introduction to the rigorous theory of the continuum." - Science Progress "Extremely readable . . . a clear axiomatically constructed introduction." - Elemente der Mathematik This classic of mathematics presents the best systematic elementary account of the modern theory of the continuum as a type of serial order. Based on the Dedekind-Cantor ordinal theory, this text is suitable for advanced undergraduates and graduate students in mathematics and requires no knowledge of higher mathematics. The treatment begins with a historical introduction, followed by chapters on classes in general; simply ordered classes, or series; discrete series, especially the type of the natural numbers; and dense series, especially the type of the rational numbers. Subsequent chapters explore continuous series, especially the type of the real numbers; continuous series of more than one dimension, with a note on multiply ordered classes; and well-ordered series, with an introduction to Cantor's transfinite numbers. An Index of Technical Terms concludes the text. AUTHOR: E. V. Huntington (1874 1952) taught at Harvard from 1901 until his retirement in 1941. He was President of the Mathematical Association of America in 1919 and at different times an officer of the American Mathematical Society and the American Association for the Advancement of Science.