Autonomous vehicles will benefit from the ability to perform aggressive driving maneuvers in safety-critical situations where the full use of available tire-road friction is required. Unfortunately, vehicle steering dynamics become highly nonlinear and difficult to model near the limits of tire adhesion, making accurate control of these maneuvers difficult. One promising approach is to use iterative learning control (ILC) as a method of gradually determining the proper steering input for a transient driving maneuver by repeating the maneuver several times and using information from previous iterations to improve the reference tracking performance. This paper explores the viability of this concept by applying learning algorithms for multiple-lap path tracking of an autonomous race vehicle. Racing is an ideal scenario for iterative learning control because race cars drive the same sequence of turns while operating near the physical limits of tire-road friction. This creates a repeatable set of nonlinear vehicle dynamics and road conditions from lap to lap. Simulation results are used to design and test convergence of both a proportional-derivative (PD) and quadratically optimal (Q-ILC) iterative learning controller, and experimental results are presented on an Audi TTS race vehicle driving several laps around Thunderhill Raceway in Willows,CA at combined vehicle accelerations of up to 8 m/s2. Both control algorithms are able to correct transient path tracking errors and significantly improve the performance provided by a reference feedforward controller.