Relationship between symmetries and conservation laws

The fundamental relation between Lie-Backlund symmetry generators and conservation laws of an arbitrary differential equation is derived without regard to a Lagrangian formulation of the differential equation. This relation is used in the construction of conservation laws for partial differential equations irrespective of the knowledge or existence of a Lagrangian. The relation enables one to associate symmetries to a given conservation law of a differential equation. Applications of these results are illustrated for a range of examples.