p-adic Numbers: An Introduction (Universitext)

From the reviews:

This is a well-written introduction to the world of p-adic numbers. The reader is led into the rich structure of the fields Qp and Cp in a beautiful balance between analytic and algebraic aspects. The overall conclusion is simple: an extraordinarily nice manner to introduce the uninitiated to the subject. Not only giving the background necessary to pursue the matter, but doing it in such a way that a healthy 'hands-on experience'is generated in the process. Mededelingen van het wiskundig genootschap

It is perhaps the most suitable text for beginners, and I shall definitely recommend it to anyone who asks me what a p-adic number is. The Mathematical Gazette

From the reviews of the second edition:

If I had to recommend one book on the subject to a student - or even to a fully grown mathematician who had never played with p-adic numbers before - it would still be this book. ... Gouvea has succeeded admirably in taking a topic that is not standard in the undergraduate mathematics curriculum and writing a book accessible to undergraduates that allows its reader to play with some intriguing mathematics and explore a topic which is both fun and important. (Darren Glass, The Mathematical Association of America, January, 2011)