Human-robot interaction requires good coordination so that the human and robot can perform their tasks without interruption. Most importantly, the robot needs to be able to react to movements of the human in order to prevent harm to the human or objects. A basic necessity is tracking of the current position of the human and objects. For this, existing motion tracking systems can be used to track both the human and objects in the environment. In addition, information about future movements can be useful to improve the interaction. In this thesis, methods for detection and prediction of human activities using machine learning are developed and evaluated. Our system can discern a set of different activities based on 3-dimensional position data of objects and the human skeleton together with the eye gaze direction. Further, it generates trajectories of possible future movement for each of these activities. These are scored in order to anticipate the most likely activity in the near future. Our results show an improvement in activity recognition performance from using gaze data.