THE aim of this translation is to reproduce, as far as possible, the ideas and style of the original in idiomatic English, rather than to give a literal rendering of its contents. Even the verbal deviations, however, are few in number. So little has been written in English on the subject that a standard set of technical terms as yet hardly exists. Where there was any choice between equivalent words, I have followed the usage of Dr Forsyth in his recently published work on the Theory of Functions. A Glossary of the principal technical terms is appended, giving the original German word together with the English adopted in the text.