Abstarct: In this thesis, we study Lie symmetry method for partial differential equations to find symmetry groups, invariant solutions, exact solutions and general solutions. Also, we show how to make local conservation laws arises from a system of differential equations by using direct method, This operation is baxsed on finding of the first conservation laws multiples that played major role in this thesis. At the end, the relations between conservation laws and point symmetries of PDEs are given.