The development of adaptive control design techniques for nonlinear systems with parametric uncertainty has been intensively studied in recent years. The recently developed adaptive backstepping technique has provided a systematic solution to the problem of designing static adaptive controllers for uncertain nonlinear systems transformable into the triangular Parametric Strict Feedback and Parametric Pure Feedback forms. The adaptive backstepping technique has been adopted in this thesis as the control design approach and a number of new algorithms have been developed for the design of dynamical controllers for the regulation and tracking of deterministic and adaptive control systems. The combination of adaptive backstepping and Sliding Mode Control has also been proposed to design robust adaptive strategies for uncertain systems with disturbances. The class of adaptive backstepping nonlinear systems has been broadened to observable minimum phase systems which are not necessarily transformable into tri- angular forms. The design of output feedback control, when only the output is measured, has also been studied for a class of uncertain systems transformable into the adaptive generalized observer canonical form. Since the equations arising from these new algorithms are too complicated to be computed by hand, a symbolic algebraic toolbox has been developed. This toolbox implements the proposed algorithms for the design of static (dynamic) deterministic (adaptive) controllers, and automatically generates MATLAB code programs for computer simulation.