Autonomous unmanned aerial vehicles (UAVs) that can execute aggressive (i.e., high-speed and high-acceleration) maneuvers have attracted significant attention in the past few years. This article focuses on accurate tracking of aggressive quadcopter trajectories. We propose a novel control law for tracking of position and yaw angle and their derivatives of up to fourth order, specifically velocity, acceleration, jerk, and snap along with yaw rate and yaw acceleration. Jerk and snap are tracked using feedforward inputs for angular rate and angular acceleration based on the differential flatness of the quadcopter dynamics. Snap tracking requires direct control of body torque, which we achieve using closed-loop motor speed control based on measurements from optical encoders attached to the motors. The controller utilizes incremental nonlinear dynamic inversion (INDI) for robust tracking of linear and angular accelerations despite external disturbances, such as aerodynamic drag forces. Hence, prior modeling of aerodynamic effects is not required. We rigorously analyze the proposed control law through response analysis and demonstrate it in experiments. The controller enables a quadcopter UAV to track complex 3-D trajectories, reaching speeds up to 12.9 m/s and accelerations up to 2.1 g, while keeping the root-mean-square tracking error down to 6.6 cm, in a flight volume that is roughly 18 m <inline-formula> <tex-math notation="LaTeX">\times 7 </tex-math></inline-formula> m and 3-m tall. We also demonstrate the robustness of the controller by attaching a drag plate to the UAV in flight tests and by pulling on the UAV with a rope during hover.