Posting has slowed a little bit this month because of holidays, but in the last couple weeks during my visit home I decided to refresh some basic knowledge of valuation theory by going through thoroughly the book “Introduction to *p*-adic Numbers and Valuation Theory” by George Bachman. Naturally, I wrote this quick review.

Bachman’s book is designed to be a leisurely introduction to valuation theory and *p*-adic numbers. It has only 152 pages and naturally cannot be comprehensive. It is, rather, an enjoyable read that does not require much advanced knowledge, though some experience with metric spaces is certainly required to fully appreciate the later chapters on the extension of valuations.

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