Synchronous oscillatory behavior is a hallmark of electrical activity in cortical neuronal networks and the brain in general. There is increasing evidence that synchronous oscillations play fundamental roles in cognition and neural information processing, but their exact functional roles remain unclear. To understand how the oscillations contribute to cognitive function, it is critical to understand how the intrinsic properties of neurons and the network connectivity shape rhythmic synchronous activity in neuronal networks. Inhibitory interneurons, which form sub-networks via weak but extensive electrical coupling, appear to play essential roles in producing synchronous oscillations in the brain. We will use a combination of numerical simulations and mathematical analysis, as well as data from in vitro experiments, to determine conditions that promote robust synchrony and those that can disrupt synchrony in electrically coupled networks of interneurons. Specifically, we will use phase response properties of neurons and the theory of weakly coupled oscillators to dissect out the influences of specific membrane conductances on synchronization. We will also use large-scale network simulations, analytical techniques in the weak coupling limit, and an approach involving master stability functions to determine how network structure influences the spatial properties of synchronization. The brain is composed of large inter-connected networks of neurons. Synchronous oscillatory activity in these networks of neurons is a hallmark of electrical activity in the brain. Synchronous activity is thought to play fundamental roles in many cognitive processes, and its disruption has been linked to complex neurological disorders such as schizophrenia and autism. In order to understand how the synchronous oscillations contribute to cognitive function, it is critical to identify the cellular mechanisms underlying them. Subnetworks of inhibitory neurons that are extensively connected via "electrical coupling" appear to play essential roles in producing the synchronous oscillations in the brain. Synchrony in these inhibitory networks is determined by connectivity in the network and intrinsic electrical properties of the cells. However, it is still unclear how these features combine to set the level of synchrony in the network and its spatial extent. Using a combination of mathematical modeling, computer simulations and theoretical analysis, as well as experimental data, we will study the mechanisms of synchrony in electrically coupled networks of inhibitory neurons and determine conditions that promote synchrony and those that can disrupt synchrony. We will determine the influences of specific membrane channels that could be targets of drug therapies. We will also examine how the structure of the network influences synchronization. This work will be part of a large body of research that will lead to improved treatments for complex neurological disorders such as epilepsy, schizophrenia and autism.