The term Set Theoretic Analysis, though loosely used for a long time, was never declared as any specific branch of mathematics. So, why bother to make this website?
It is my belief, that in recent years there has been a large number of results that should be put precisely under this heading. I have collected some of them in my recent survey, which can be considered as an introduction to the subject.
In few words, the new aspect of this research is the use of modern set theoretical methods to study (mostly pathological) real functions. This distinguishes set theoretic analysis from descriptive set theory, whose objects of study are various classes of (mostly nice) sets and their hierarchies, such as Borel sets or analytic sets. However, the more traditional variations of set theoretical analysis, including descriptive set theory, the duality between measure and category, and the studies on "small" subsets of reals, should also become a part of this site.