Analyzing and understanding human motion is a major research problem widely investigated in the last decades in various application domains. In this work, we address the problem of human motion analysis in the context of kinaesthetic rehabilitation using a robot coach system which should be able to learn how to perform a rehabilitation exercise as well as assess patients' movements. For that purpose, human motion analysis is crucial. We develop a human motion analysis method for learning a probabilistic representation of ideal movements from expert demonstrations. A Gaussian Mixture Model is employed from position and orientation features captured using a Microsoft Kinect v2. For assessing patients' movements, we propose a real-time multi-level analysis to both temporally and spatially identify and explain body part errors. This allows the robot to provide coaching advice to make the patient improve his movements. The evaluation on three rehabilitation exercises shows the potential of the proposed approach for learning and assessing kinaesthetic movements.