We present BrainNet which, to our knowledge, is the first multi-person non-invasive direct brain-to-brain interface for collaborative problem solving. The interface combines electroencephalography (EEG) to record brain signals and transcranial magnetic stimulation (TMS) to deliver information noninvasively to the brain. The interface allows three human subjects to collaborate and solve a task using direct brain-to-brain communication. Two of the three subjects are designated as "Senders" whose brain signals are decoded using real-time EEG data analysis. The decoding process extracts each Sender's decision about whether to rotate a block in a Tetris-like game before it is dropped to fill a line. The Senders' decisions are transmitted via the Internet to the brain of a third subject, the "Receiver," who cannot see the game screen. The Senders' decisions are delivered to the Receiver's brain via magnetic stimulation of the occipital cortex. The Receiver integrates the information received from the two Senders and uses an EEG interface to make a decision about either turning the block or keeping it in the same orientation. A second round of the game provides an additional chance for the Senders to evaluate the Receiver's decision and send feedback to the Receiver's brain, and for the Receiver to rectify a possible incorrect decision made in the first round. We evaluated the performance of BrainNet in terms of (1) Group-level performance during the game, (2) True/False positive rates of subjects' decisions, and (3) Mutual information between subjects. Five groups, each with three human subjects, successfully used BrainNet to perform the collaborative task, with an average accuracy of 81.25%. Furthermore, by varying the information reliability of the Senders by artificially injecting noise into one Sender's signal, we investigated how the Receiver learns to integrate noisy signals in order to make a correct decision. We found that like conventional social networks, BrainNet allows Receivers to learn to trust the Sender who is more reliable, in this case, based solely on the information transmitted directly to their brains. Our results point the way to future brain-to-brain interfaces that enable cooperative problem solving by humans using a "social network" of connected brains.