In this thesis, kinematic and dynamic adaptive control in the case of unknown kinematic and dynamic structure of robotic systems was investigated. The main work involved defining a new type of kinematic inversion scheme in the case of trajectory control that would remove the need for a Jacobian with full row rank for convergence purposes. As further work, a method for constructing kinematic and dynamic regressors for robot systems whose structure is unknown is presented. Finally, simulations are presented that demonstrate the effectiveness of the developed kinematic control applied to robotic systems with unknown kinematic and dynamic structure.