Tutorials in Mathematical Biosciences I : Mathematical Neuroscience Preface A. Friedman: Introduction to Neurons D. Terman: An Introduction to Dynamical Systems and Neuronal Dynamics B. Ermentrout: Neural Oscillators A. Borisyuk: Physiology and Mathematical Modeling of the Auditory System. This volume introduces some basic theories on computational neuroscience. Chapter 1 is a brief introduction to neurons tailored to the subsequent chapters. Chapter 2 is a self contained introduction to dynamical systems and bifurcation theory oriented towards neuronal dynamics. The theory is illustrated with a model of Parkinsons disease. Chapter 3 reviews the theory of coupled neural oscillators observed throughout the nervous systems at all levels; it describes how oscillations arise what pattern they take and how they depend on excitory or inhibitory synaptic connections. Chapter 4 specializes to one particular neuronal system namely the auditory system. It includes a self contained introduction from the anatomy and physiology of the inner ear to the neuronal network that connects the hair cells to the cortex and describes various models of subsystems.