This thesis is primarily concerned with a normal form characterization for normal forms of ordinary differential systems and control systems. The normal form characterization here follows an important normal form style that is called inner product normal form style. A normal form characterization for normal forms can be obtained by driving and solving a corresponding linear partial differential equation. We recall the method of characteristics for solving the corresponding linear PDEs. In this direction, the relation between the characteristic curves and first integrals of the corresponding differential system of equations are illustrated. The first part relies on the results on ODEs and is based on results developed by elphick et.al while the characterization for control systems follows the generalization of the results on the ODE system for nonlinear control systems. The latter is implemented and described by Hamzi et.al. The result are applied on a general linearly controllable system. The characterization of normal forms for these systems are presented. The control systems in the vicinity of an uncontrollable equilibrium is also considered. The introduced method is applied on two examples in order to show the method can be applied to linearly uncontrollable cases. The second part of this thesis focuses on a normalization method for control system, that is called pull-up and push-down methods. Simultaneous application of pull-up and push-down methods on a control system provides a complete normalization process. These methods are applied an a variety of examples to illustrate their applicability.