I would like a challenging and complete introduction to $p$-adic numbers (as I eventually plan to study $p$-adic geometry). I understand that Gouvêa’s book is popular, however, I’m sure that there are lesser-known texts that are high quality as well.
2026-03-29 09:18:57.1774775937
Bumbble Comm
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$p$-adic Numbers Textbook Suggestions
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There are some good books I know. I am listing them.
(1) p-adic Numbers: An Introduction by Fernando Q. Gouvêa
(2) A Course in p-adic Analysis by Alain M. Robert
(3) Introduction To p-adic Analytic Number Theory by M Ram Murty
Also, there is a recent open lecture-note Introduction To p-adic Numbers and p-adic Analysis by Andrew Baker in AMS open math notes.
Hope it will help.
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Serre, Local Fields (or the French original Corps Locaux which as far as I recall has fewer typos).
Schikhof, Ultrametric Calculus.
Fesenko / Vostokov, Local Fields and their Extensions
Cassels, Local Fields.
Some texts on local class field theory (Iwasawa; Neukirch) also contain short, succinct introductions.