The standard playground for a lot of analysis is $L^{p}$ spaces. These function spaces have great global properties (in terms of their relationships with each other and inequalities that connect them) but typically have very bad local properties (most of their constituent functions are extremely rough). Instead, we will look at some $L^{p}$ spaces of holomorphic (aka complex analytic) functions. These spaces have extremely nice local properties: their elements are as smooth as can be, and they moreover satisfy universal growth estimates you might not expect. By contrast, their global properties are not as nice: for example, they are not related to their dual spaces in the way one might expect. We'll discuss some of these dichotomies and try to give the flavor of modern research in holomorphic spaces. And we'll discover the truth about the delta function...