Whilst the greatest effort has been made to ensure the quality of this text, due to the historical nature of this content, in some rare cases there may be minor issues with legibility. The present edition of this volume has been carefully revised and corrected throughout. The principal alterations will be found in the Theory of Series; which has been developed a little in some places, with a view to rendering it more useful to students proceeding to study the Theory of Functions. In the interest of the same class of readers.