Basic Experimental Facts and Theoretical Tools.- The Neuron - Building Block of the Brain.- Neuronal Cooperativity.- Spikes, Phases, Noise: How to Describe Them Mathematically? We Learn a Few Tricks and Some Important Concepts.- Spiking in Neural Nets.- The Lighthouse Model. Two Coupled Neurons.- The Lighthouse Model. Many Coupled Neurons.- Integrate and Fire Models (IFM).- Many Neurons, General Case, Connection with Integrate and Fire Model.- Phase Locking, Coordination and Spatio-Temporal Patterns.- Phase Locking via Sinusoidal Couplings.- Pulse-Averaged Equations.- Conclusion.- The Single Neuron.- Conclusion and Outlook.

This book addresses a large variety of models in mathematical and computational neuroscience. It is written for the experts as well as for graduate students wishing to enter this fascinating field of research. The author studies the behaviour of large neural networks composed of many neurons coupled by spike trains. An analysis of phase locking via sinusoidal couplings leading to various kinds of movement coordination is included.