Eltayeb Ali Adam Beady2018-10-082018-10-082014http://hdl.handle.net/123456789/13099A Thesis Submitted in Fulfillment for the Degree of Philosophy in Mathematics (Sciences)Abstract In this research we dealt with the theory of Exterior differential systems and it‘s applications. In particular we were concerned with applications to partial differential equations. A Several approaches have been discussed, including Cartan equivalence method, Lie symmetry-method and Cartan-Kahler mefl1od. Our main problem has been the existence of integral manifolds of some integral elements. The uniqueness problem has also been treated. We have illustrated our notions, theorems and techniques with some examples.endifferential systemsThesis