A fuzzy multifunction is a fuzzy set valued function. Fuzzy multifunctions arise in many applications, for instance, the budget multifunction occurs in economic theory, artificial intelligence and decision theory. The biggest difference between fuzzy functions and fuzzy multifunctions has to do with the definition of an inverse image. For a fuzzy multifunction there are two types of inverses. These two definitions of the inverse then leads to two definitions of continuity. Papageorgiou (1985), introduced the notion of fuzzy multifunction and extended the concepts of fuzzy continuous functions to the fuzzy multivalued case, by introducing of fuzzy upper (lower) semi-continuous multifunctions. In 2015, Ramadan and Abd El-latif, introduced and studied the concepts of fuzzy upper (lower) almost continuous, weakly continuous and semi-continuous multifunctions where the domain of these functions is a classical topological space with their values as arbitrary fuzzy sets in fuzzy topological space. The purpose of this book is to introduce and study many forms of fuzzy upper (lower) continuous multifunctions where both domain and codomain are fuzzy topological spaces in Sostak's sense.