This is a presentation on mathematical neuroscience which explores the behaviour of neural systems using a dynamical systems approach at multiple scales. This presentation begins with a discussion of action potential generation in single cells, following the seminal work of Hodgkin and Huxley, before moving through analysis of axonal and dendritic dynamics, before ending at descriptions of large-scale brain regions. At these scales, the presentation also covers typical measurement approaches, such as EEG, and discusses the relevance of the measured signals to human behaviour.