Abstract: A fundamental idea in number theory is to, given some equation, reduce it modulo some number. This is a fertile source of information: this is how one tells that, for example every prime greater than 2 that is the sum of two squares must be 1 mod 4. The subject of this talk will be the p-adic integers, which give us a way to leverage all of this information about an equation modulo some numbers. I will go over a few definitions, some basic properties and hopefully the above picture, which depicts the metric on the 3-adic integers.