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. The remaining three chapters definitely demand more mathematical maturity on the part of the reader. At least a first course in modern algebra would be required to read parts of them. (From author's preface)