A text primarily for beginning graduate students that is largely an account of mainstream theory but also contains some illustrative applications. Algebraic number theory, originally developed to attack Fermat's Last Theorem, has become an important tool over a wide range of pure mathematics, and many of the ideas involved generalize to branches such as algebraic geometry. The text covers the two basic methods of approaching algebraic number theory: using ideals and valuations. The author is a Cambridge (UK) mathematician.

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