A graduate text introducing algebraic number theory and extending it to algebraic functions of a single variable. Koch assumes readers to have a good knowledge of linear algebra and field theory. His treatment goes to up, but barely mentions, class field theory and so should prepare students to embark on research at any level below that. In elucidating the principles, he recapitulates the historical development of the field. The original Zahlentheorie was published by Friedr, Vieweg, and Sohn, Wiesbaden, in 1997. Annotation copyrighted by Book News, Inc., Portland, OR