What is the theme of analysis? It is safe to say that every mathematician, at some point in their career, has had some form of exposure to analysis. Quite often, it appears first in the form of an undergraduate course in real analysis. It is there that one is often exposed to a rigorous viewpoint to the techniques of calculus that one is already familiar with. At this stage, one might argue that real analysis is the study of real numbers, but is it? A big chunk of it involves algebraic properties, and as such lies in the realm of algebra. It is the order properties, though, that do have a sort of analysis point of view. Sure, some of these aspects generalise to the level of topologies, but not all. Completeness, for one, is clearly something that is central to analysis.
Similar arguments can be made for complex analysis and functional analysis.
Now, the question is: As for all the topics that are bunched together as  analysis, is there any central theme to them? What topics would you say that belongs to this theme? And what are the underlying themes in these individual subtopics?
Add. It may be a subjective question, but having a rough idea of what the central themes of a certain field are helps one to construct appropriate questions. As such, I think it is important. I am not expecting a single answer, but more of a diverse set of opinions on the matter.

Mathematical analysis is a mental edifice built up to describe and understand phenomena of geometry, physics, and technics in terms of formulas involving finite mathematical expressions. The core of this all is the study of functions $f:\>{\mathbb R}\to{\mathbb R}$ and their properties.
