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A few recommendations: Fernando Q. GouvĂȘa's $p$-adic numbers: An Introduction. This text gives a good introduction to the $p$-adic number system and the properties of the space of $p$-adic numbers, vector spaces over $\mathbb{Q}_p$, and the metrically completed algebraic closure of $\mathbb{Q}_p$. There is also some discussion of $p$-adic analysis near ...


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There's a really nice book by Svetlana Katok called "p-adic analysis compared to Real."


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