Carnap’s quasi-analysis is usually considered as an ingenious but definitively flawed approach in epistemology and philosophy of science. In this paper it is argued that this assessment is mistaken. Quasi-analysis can be reconstructed as a representational theory of constitution of structures that has applications in many realms of epistemology and philosophy of science. First, existence and uniqueness theorems for quasi-analytical representations are proved. These theorems defuse the classical objections against the quasi-analytical approach launched forward by Goodman and others. Secondly, the (...) constitution of various kinds of structures is treated in detail: order structures, comparative similarity structures, mereological, mereotopological, and topological structures are considered. In particular, it is pointed out that there exist interesting relations between quasi-analysis and modern theories of pointless topology. (shrink)