الفهرس 
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Abstract
In this thesis, we studied and investigated the concept of soft sets and their properties. Mainly, we evolve the concept of soft elements of soft sets. Also, we proposed a refinement for the concept of soft mappings to study the surjections, injections, and bijections of soft mappings. Furthermore, we investigated the soft algebraic system such as soft groups, soft rings, and soft modules. Besides, we introduced soft modules over soft rings and explored their basic features. Moreover, we investigated and analyzed the concept of soft topology and its components and introduced a new version of the soft continuity of soft mappings over soft topological spaces. Also, we introduced the concepts of soft topological groups and soft topological soft groups and their subsystems by applying the soft continuity over the group and soft groups. Furthermore, we introduced the concepts of soft topological rings and soft topological soft rings and their subsystems by applying the soft continuity over the rings and soft rings. Moreover, we introduced soft topological modules and soft topological soft modules and their subsystems by applying the soft continuity over the modules and soft modules. On the other hand, we generalized the concept of soft numbers and developed many well-known theorems over integers to deal with the soft theory, like the Chinese remainder theorem over the soft integers beside many other approaches. Finally, we introduced the ring of soft 𝑝ˆ-adic numbers, which represent sequences of soft numbers that generate a soft metric space under some conditions called soft 𝑝ˆ- metric spaces.