The fuzzy set theory has been initiated by the seminal work published by Lotfi A. Zadeh in 1965 and since then, it attracted numerous researchers and scholars. The main impact was, that it led to an extensive research of fuzzy modelling methods, i.e., methods of modelling real situations by the use of fragments of the fuzzy set theory. And therefore, there was a big demand to develop firm theoretical backgrounds establishing fundamentals for the application oriented fuzzy modelling area. In this talk, we will guide students form the most elementary fundamentals of the fuzzy set theory through the algebraic as well as analytical backgrounds of the area and finally, leading to the foundations of the most usual fuzzy models.