On Noether Symmetries and Conservation Laws

Noether symmetries provide conservation laws that are admitted by Lagrangians representingphysical systems. For differential equations possessing Lagrangians these symmetries are obtained by the invariance of the corresponding action integral. This work introduces briefly the basic theory of Lie groups, Lie algebra and Lie point symmetry of DEs. Also it provides the basic concepts, definitions and theorems required to find Noether symmetries and the corresponding conservation laws. The main concern of this thesis is finding Noether symmetries and conserved vectors for a Lagrangian corresponding a particular metric, known as Milne model and comparing them with the isometries of this metric. we also construct wave equation on this metric and obtain its Lie point symmetries.