Runda Abdalhafiz Abdelrhim . Bashir2018-11-122018-11-122014http://hdl.handle.net/123456789/13538A Thesis Submitted In Fulfillment For PhD .Degree In MathematicsAbstract In this research we considered Cartans equivalence problem . We defined the concept of equivalence and illustrated that by several cases . We introduced the equivalence problem for Coframs and then used Cartans equivalence method to determine whether two differential operators are equivalent , we also handle the classification problem of Lie algebras, ln particular we treated the case of semi-simple Lie algebras.enThe Formulation Of EquivalenceThesis