The rapid evolution of the on-line world over the past decade represents a blending of social and technological networks, and it is changing the ways in which we interact with information and with each other. It is also the leading edge of a revolution in measurement, with the digital traces of on-line interaction enabling the study of social processes at unprecedented levels of scale and resolution.

Making sense of this kind of data, and using it to shape the networks we inhabit, raise many new questions --- among them, how to synthesize information when there are a billion sources providing it; how to reason about privacy in a world where almost every transaction is recorded; and how to develop the scientific principles that can relate individual behavior to global properties of large populations. The resulting challenges require new ideas in mathematics, computing, and the social sciences, and point to opportunities at the emerging interface of these disciplines.