In the present new edition only slight changes are made, consisting of brief additions, more numerous examples, different modes of expression, and the like. In reference to the above extract from the preface of the preceding edition, I have asked myself the question, whether I should not from the beginning adopt the original Riemann enunciation of the fundamental proposition instead of that which is given in § 49. Nevertheless, I have finally adhered to the previous arrangement, because I think that in this way the difference between the two enunciations is made more prominent, and the advantages of the Riemann enunciation are more distinctly emphasized.