One of the aims of study the fuzzy set theory is to develop the methodology of the formulations and the solutions of problems that are too complicated or ill-defined to be acceptable to analysis by conventioal techniques. Therefore, fuzziness could be considered as a type of imprecision that steams from a grouping of elements into classes that do not have exact defined boundaries. Such classes, introduced by Zadeh L. A., in 1965 as a tool used to describe the ambiguity, vagueness and ambivalence in the mathematical models.This thesis have three objectives. The first objective is to study fuzzy sets theory and presenting the proof of some well known results in this theory which are either not proof previously or the proofs are not given in details. The second objective is to study and proof the existence and uniqueness theorem of fuzzy differential equations using Schauder fuzzy fixed point theorem. The third objective is to give an initial introduction of the subject of Boundary Value Problems of Fuzzy Differential Equations which had not been introduced previously, as well as, some methods of solution of such type of problems.
