The nervous system of higher animals is very complex and highly nonlinear. among its many capabilities are making decisions and carrying out complex motor actions such as swimming. Nonlinear dynamical modelling can be used to understand and explain neural phenomena at many different levels, including - ion-currents and action potentials; short - and long - term memory; visual hallucinations; neural synchronization; motor control This book explores the mathematical principles by which brains generate spikes, make decisions, store memories, and control actions. It assumes a basic knowledge of calculus and develops the dynamical foundations of neuroscience using problem sets and computer simulations on the accompanying PC and Mac compatible MatLab disk.