a quadrotor is a type of unmanned aerial vehicles. it has been widely used in aerial photography. the quadrotor has the capability of vertical takeoff and landing, which is very useful in small or narrow areas. the mechanical structure of a quadrotor is also simple, which makes it easy to produce and maintain. it is a strong candidate for a future means of transportation. in practical applications, it is commonly controlled by a proportional integral derivative controller. in this thesis, two nonlinear controllers are designed to control the attitude and the position of a quadrotor by using the backstepping technique. the attitude is estimated by a nonlinear attitude estimator, which is based on a nonlinear explicit complementary filter. it uses data from a six axis inertial measurement unit and a three axis magnetometer to calculate the estimated attitude. to avoid the singularity problem like "gimbal lock" in euler angle attitude representation, the unit quaternion attitude representation is applied in the controller derivation. however, the euler angle representation is easier for people to imagine the actual attitude of a quadrotor. to make it more readable, the results of the experiments are converted to the euler angle representation. during the derivation of a backstepping controller, a neural-network is applied to estimate the nonlinear terms in the system. the universal approximation theorem is the principle for the estimation of nonlinear terms. besides, a two step controller is derived by modifying the backstepping controller with four steps. the two step controller is developed by an adaptive method for both the nonlinear terms and the moment of inertia. analysis shows the boundedness of the closed-loop system with both controllers. finally, the proposed controllers are tested on a true quadrotor system. experimental results show the effectiveness of the two proposed controllers. also, comparison between two controllers are carried out. in addition, some future works are discussed.