The theory of complex analysis in one variable is in some sense the calculus student's dream come true. No annoying pathological cases, and things generally just work right. However the zero sets of analytic functions in one variable are downright boring (isolated points). In this talk I will talk about the Hartogs Phenomenon which has a coolness factor at least double that of the Maximum Principle. In particular it will tell us something about how the zero sets of analytic functions behave when we have more than one complex variable. You will also find out what the inhomogeneous d-bar equation is, and how to exhibit solutions in certain cases, which should really come in handy next time you are in a bar and need to show off something more impressive than flipping ten beer coasters at once. This talk should be accessible to all who have not slept through basic calculus (or at least not slept through most of it).