The Brain Dynamics Toolbox is open-source matlab software for simulating dynamical systems in neuroscience. Specifically, initial-value problems in systems of Ordinary Differential Equations (ODEs), Delay Differential Equations (DDEs), Stochastic Differential Equations (SDEs) and Partial Differential Equations (PDEs). Users define their system of equations as a custom function. Interchangeable solvers and graphical plotting tools can then be applied to that system with no additional programming effort. The graphical interface allows the dynamics to be explored interactively, while the command-line tools allow large-scale simulations to be scripted. This book is for researchers and students who wish to use the toolbox to simulate their own dynamical models in matlab. It describes how to program the dynamical equations and run them using both the graphical interface and the command-line tools. The source code for the finished model can be disseminated independently of the toolbox.