Collective organization appears everywhere. In the natural world, blind army ants coordinate a massive raid across a rainforest floor, a flock of birds arcs and ripples while descending to roost, and a school of fish convulses as if one entity when threatened. We too are integrated in collective self-organized behavior -- in traffic flow, social networks, and crowd movement in a densely populated spatial framework. This symposium uses mathematical modeling and simulation to show how collective self-organized behavior arises and why it is so pervasive in nature and human society. The properties and dynamics of such aggregate systems will be developed and illustrated using different methods and interdisciplinary perspectives. Models and analyses of collective biological systems may be adapted toward developing robot swarms whose individuals transmit information to each other or to a central observer. Cooperative robot swarms have many important applications, since they can overcome biological limitations and can be sent into environments inaccessible or too dangerous for humans. (A robot fleet of cooperating sensors, for example, was used to monitor algae blooms in Monterey Bay, CA.) This multidisciplinary symposium is intended to be accessible to a general scientific audience.