Despite the increasing popularity of route guidance systems, current digital maps are still inadequate for many advanced applications in automotive safety and convenience. Among the drawbacks are the insufficient accuracy of road geometry and the lack of fine-grained information, such as lane positions and intersection structure. In this paper, we present an approach to induce high-precision maps from traces of vehicles equipped with differential GPS receivers. Since the cost of these systems is rapidly decreasing and wireless technology is advancing to provide the communication infrastructure, we expect that in the next few years large amounts of car data will be available inexpensively. Our approach consists of successive processing steps: individual vehicle trajectories are divided into road segments and intersections; a road centerline is derived for each segment; lane positions are determined by clustering the perpendicular offsets from it; and the transitions of traces between segments are utilized in the generation of intersection models. This paper describes an approach to this complex data-mining task in a contiguous manner. Among the new contributions are a spatial clustering algorithm for inferring the connectivity structure, more powerful lane finding algorithms that are able to handle lane splits and merges, and an approach to inferring detailed intersection models.