The nervous system of higher animals is both very complex and very nonlinear. Nervous systems are constantly making decisions between alternative actions, and switching gears among dynamical modes. This book is an exploration of the mathematical principles by which brains generate neural spikes, make decisions, store memories, and control actions. Assuming only a basic knowledge of mathematics, and including problem sets and simulations on disk, Spikes, Decisions, and Actions is an ideal text for courses in neuronal modelling in particular, and mathematical modelling in biology generally.