The field of p-adic numbers forms a bridge from number theory to analysis, mixing number-theoretic constructions with analytic ideas. And just as the complex numbers made possible complex analytic geometry, the p-adic numbers opened up a new, strange geometry over a number-theoretic field. 

The goal of this talk is to paint a broad picture of p-adic geometry accessible to mathematicians without any previous knowledge of number theory. We set the foundations with an intuitive introduction to the field of p-adic numbers and then give a brief introduction to so-called rigid geometry, the p-adic counterpart to complex analytic geometry.