Zadeh (1965), introduced the basic idea of a fuzzy set as an extension of classical set theory. In 1968, Chang was the first to introduce the concept of a fuzzy topology. Kubiak and Sostak (1985) introduced the fundamental concept of a fuzzy topological structure, as an extension of both crisp topology and fuzzy topology, in the sense that not only the objects are fuzzified, but also the axiomatics. Also, Sostak gave some rules and showed how such an extension can be realized. The purpose of this book is to introduce and study some new definitions of fuzzy sets, continuous mappings and separation axioms On Fuzzy Topological Spaces In Sostak's Sence.