This dissertation describes a novel system for the perception and prediction of urban traffic scenarios for autonomous driving. It is based on the AutoNOMOS self driving car project of the Freie Universität Berlin. The system combines best practices with new methods and findings. The description and evaluation of these new methods and findings form the main contributions of the thesis. These contributions are evaluated using real-world traffic scenarios recorded during test drives with the self driving vehicle MadeInGermany of the FU Berlin. Since the system also handles very complex and potentially dangerous traffic scenarios, a simulation environment has been developed to evaluate the system also under such conditions. The perception system uses a LIDAR device which readings are processed as range image. The first contribution of this work is a new algorithm to identify pixels originating from the ground which is proven to be more efficient than existing methods. The tracking of moving objects is often done by Kalman filters and many previous publications propose to use curvilinear motion models for these filters. The evaluation of real-world traffic scenarios proves, that theses motion models are unsuitable for urban traffic, since the filters get unstable at slow velocities. A new algorithm, which very efficiently calculates the collision probability between two rectangular objects, is the third contribution. The main contribution of this work is a new rule-based interaction-aware multi-modal prediction method for urban traffic scenarios. The method takes into account all classes of traffic participants as cars, trucks, bicycles and pedestrians and handles all relevant types of motion behaviors, as car following, lane changes and merges, turning and intersection crossing. The system is able to predict very complex urban scenarios with several dozen agents for 10 seconds and more at a frequency of 10 Hz. The last contribution is a simulation system which allows to evaluate the prediction results also in dangerous scenarios and furthermore to show that the generated prediction can also be useful for the local behavior planning of an autonomous vehicle.