Introduction

This book is an introduction to the theory of algebraic numbers and algebraic functions of one variable. The basic development is the same for both using E Artin's elegant approach, via valuations.

Number Theory

Number Theory is pursued as far as the unit theorem and the finiteness of the class number.

Function Theory

In function theory the aim is the Abel-Jacobi theorem describing the divisor class group, with occasional geometrical asides to help understanding.

Assuming only an undergraduate course in algebra, plus a little acquaintance with topology and complex function theory, the book serves as an introduction to more technical works in algebraic number theory, function theory or algebraic geometry by an exposition of the central themes in the subject.