In this thesis, the ideal theory of Abel Grassmann’s groupoids (briefly ??-groupoids) in the framework of Double-Framed Soft Sets (briefly ?ℱ??s) is developed. The main notions defined in this thesis are that of Double-Framed Soft Abel-Grassmann’s groupoids (briefly ?ℱ? ??-groupoids), Double-Framed Soft ideals (briefly ?ℱ?ℐs), Double-Framed Soft bi-ideals (briefly ?ℱ?ℬℐs), Double-Framed Soft interior ideals (briefly ?ℱ?ℐℐs) and Double-Framed Soft quasi ideals (briefly ?ℱ??ℐs).We also generalize ?ℱ? ??-groupoids, ?ℱ?ℐs of ??groupoids and ?ℱ?ℬℐs of ??-groupoids to (M, N)- ?ℱ? ??-groupoid, (M, N)- ?ℱ?ℐs of ??groupoids and (M, N)- ?ℱ?ℬℐs ??-groupoids respectively. We discuss these newly defined notions in regular, intra-regular, left regular and right regular ??-groupoids. These classes of ??-groupoids are characterized in terms of the newly defined notions. Since the inception of soft sets is to deal with uncertainty in the data and has many applications in decisions systems, we utilize the concept of ?ℱ??s in decision making as well. Decision makings schemes based on ?ℱ??s and ?ℱ? Expert sets have been developed.