We present a new large dataset of indoor human and robot navigation and interaction, called TH\"OR-MAGNI, that is designed to facilitate research on social navigation: e.g., modelling and predicting human motion, analyzing goal-oriented interactions between humans and robots, and investigating visual attention in a social interaction context. TH\"OR-MAGNI was created to fill a gap in available datasets for human motion analysis and HRI. This gap is characterized by a lack of comprehensive inclusion of exogenous factors and essential target agent cues, which hinders the development of robust models capable of capturing the relationship between contextual cues and human behavior in different scenarios. Unlike existing datasets, TH\"OR-MAGNI includes a broader set of contextual features and offers multiple scenario variations to facilitate factor isolation. The dataset includes many social human-human and human-robot interaction scenarios, rich context annotations, and multi-modal data, such as walking trajectories, gaze tracking data, and lidar and camera streams recorded from a mobile robot. We also provide a set of tools for visualization and processing of the recorded data. TH\"OR-MAGNI is, to the best of our knowledge, unique in the amount and diversity of sensor data collected in a contextualized and socially dynamic environment, capturing natural human-robot interactions.