This book is devoted to local and global analysis of weakly connected systems with applications to neurosciences. Using bifurcation theory and canonical models as the major tools of analysis, it presents systematic and well motivated development of both weakly connected system theory and mathematical neuroscience. Bifurcations in neuron and brain dynamics, synaptic organizations of the brain, and the nature of neural codes are among the many important issues addressed. The authors offer the reader classical results as well as some of the most recent developments in the field. The book will be useful to researchers and graduate students in various branches of mathematical neuroscience.