A switching nonlinear control system consisting of multiple Lyapunov functions and an adaptive mechanism is considered for small quadrotors. A typical quadrotor has only four actuators and six degrees of freedom (DOF) which makes it an under-actuated system. Underactuation adds constraints to the control input and complicates designing the control system. In addition, quadrotor control systems suffer from the presence of parameter uncertainty. In this work, the quadrotor's parameters are considered to be unknown but bounded. The proposed control algorithm combines a switching technique with an adaptation mechanism to overcome the difficulties associated with underactuation and uncertainty. Specifically, the switching controller is designed based on multiple Lyapunov functions to deal with the underactuation problem; and the adaptive mechanism is used to overcome the parametric uncertainties. The stability of the combined controller is proven within the region of interest, and simulation with real UAV model parameters was used to show that the proposed controller allows the system to follow a designed path closely.