A "brain defibrillator" may be closer than we think. An epileptic seizure involves a paroxysmal change in the activity of millions of neurons. Feedback control of seizures would require an implantable device that could predict seizure occurrence and then deliver a stimulus to abort it. To examine the feasibility of building such a device, this text brings together experts in epilepsy, bio-engineering, and dynamical systems theory. Topics inclu*e the development of epileptic systems, seizure prediction, neural synchronization, wave phenomena in excitable media, and the control of complex neural dynamics using brief electrical stimuli.