We describe the multi-layer temporal network which connects a population of more than 700 university students over a period of four weeks. The dataset was collected via smartphones as part of the Copenhagen Networks Study. We include the network of physical proximity among the participants (estimated via Bluetooth signal strength), the network of phone calls (start time, duration, no content), the network of text messages (time of message, no content), and information about Facebook friendships. Thus, we provide multiple types of communication networks expressed in a single, large population with high temporal resolution, and over a period of multiple weeks, a fact which makes the dataset shared here unique. We expect that reuse of this dataset will allow researchers to make progress on the analysis and modeling of human social networks.