For a class of uncertain nonlinear systems in the parametric strict feedback form, an adaptive dynamic surface control method based on the contraction theory is proposed. Every subsystem is partially contracting in the state error by designing the dynamic surface controller. The adaptive estimation via contraction is designed for the uncertain parameters. Moreover, the contraction-based singular perturbation analysis is used to reduce the subsystem dynamics, which ensures the differences of the state errors between the original and the reduced subsystems’ and the differences of the filters are bounded. By analyzing the contraction-based robustness of the hierarchical interconnection of the subsystems, it is proved that the states of the original closed-loop system can semi-globally converge to a ball centered about the desired trajectory, and it is guaranteed that both of the tracking error and adaptive estimation are bounded. Finally, simulation results of the rigid-link electrically driven robot manipulators system show the effectiveness of the proposed method