Sports and fitness exercises are an important factor in health improvement. The acquisition of new movements - motor learning - and the improvement of techniques for already learned ones are a vital part of sports training. Ideally, this part is supervised and supported by coaches. They know how to correctly perform specific exercises and how to prevent typical movement errors. However, coaches are not always available or do not have enough time to fully supervise training sessions. Virtual

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... ity (VR) is an ideal medium to support motor learning in the absence of coaches. VR systems could supervise performed movements, visualize movement patterns, and identify errors that are performed by a trainee. Further, feedback could be provided that even extends the possibilities of coaching in the real world. Still, core concepts that form the basis of effective coaching applications in VR are not yet fully developed. In order to diminish this gap, we focus on the processing of kinematic data as one of the core components for motor learning. Based on the processing of kinematic data in real-time, a coaching system can supervise a trainee and provide varieties of multi-modal feedback strategies. For motor learning, this thesis explores the development of core concepts based on the usage of kinematic data in three areas. First, the movement that is performed by a trainee must be observed and visualized in real-time. The observation can be achieved by state-of-the-art motion capture techniques. Concerning the visualization, in the real world, trainees can observe their own performance in mirrors. We use a virtual mirror as a paradigm to allow trainees to observe their own movement in a natural way. A well established feedback strategy from real-world coaching, namely improvement via observation of a target performance, is transfered into the virtual mirror paradigm. Second, a system that focuses on motor learning should be able to assess the performance that it observes. For instance, typical errors in a trainee's performa [...]