��Փ ���x

����Փ�����ݺ��飺In spite of the fact that nowadays there are quite a few books on algebraic numbertheory available to the mathematical community, there seems to be still a strongneed for a fundamental work like Hasse's ,Zahlentheorie". This impression iscorroborated by the great number of inquiries the editor received about the dateof appearance of the English translation of Hasse's book. One main reason for theunbroken interest in this book lies probably in its vivid presentation of the divisor-theoretic approach to algebraic number theory, an approach which was developedby Hasse's former teacher Hensel and further expanded by Hasse himself. Hassedoes not content himself with a mere presentation of the number-theoretic mate-rial, but he motivates the basic ideas and questions, comments on them in detail,and points out their connections with neighboring branches of mathematics. In preparing the English edition of Hasse's ��Number Theory��, I tried to pre-serve as much as possible the unique style and features of the book, even at therisk of using a partly insufficient or somewhat clumsy English. In particular,I kept the original notation of the book thus following the requirements stipulatedby Hasse. This means, e.g., that [- denotes the ring of rational integers, P thefield of rational numbers, P the field of real numbers, Pp the p-adic completionof P, and Z the field of complex numbers.