The field of p-zdic numbers, which can be obtained from the field of rational numbers by a completion process with respect to a special kind of mapping, or valuation, similar in many respects to the ordinary absolute value mapping has a great number of interesting properties. However, beyond this, it turns out that such fields are of particular interest and importance in algebraic number theory and in algebraic geometry. This is equally true of the general notion of a valuation together with some of its related concepts.
The book is meant to serve as an introduction to valuation theory. The first two chapters have been written mainly for advanced undergraduate students and first year graduate students.
The amount of algebra required is quite small, and the algebraic results needed for these two chapters are included in the first four sections of the appendix. It is hoped that in this fashion these two chapters will be reasonably self-contained and available to as wide an audience as possible. In addition, exercises have been added to these chapters most of which are intended to give the reader some manipulative facility with the concepts introintroduced.
The remaining three chapters definitely demand more mathemathematical maturity on the part of the reader. At least a first course in modern algebra would be required to read parts of them. Although most of the material needed for these chapters has been
stated in the appendix, this is meant just to serve as a handy glossary for the reader.

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