Fernando Q. Gouvea 
p-adic Numbers [PDF ebook] 
An Introduction

p-adic numbers are of great theoretical importance in numbertheory, since they allow the use of the language of analysisto study problems relating toprime numbers and diophantineequations. Further, they offer a realm where one can dothings that are very similar to classical analysis, butwith results that are quite unusual. The book should be ofuse to students interested in number theory, but at the sametime offers an interesting example of the many connectionsbetween different parts of mathematics. The book strives to be understandable to an undergraduateaudience. Very little background has been assumed, and thepresentation is leisurely. There are many problems, whichshould help readers who are working on their own (a largeappendix with hints on the problem is included). Most of all, the book should offer undergraduates exposureto some interesting mathematics which is off the beatentrack. Those who will later specialize in number theory, algebraic geometry, and related subjects will benefit moredirectly, but all mathematics students can enjoy the book.