Dynamical Systems on Networks : A Tutorial This volume is a tutorial for the study of dynamical systems on networks. It discusses both methodology and models including spreading models for social and biological contagions. The authors focus especially on “simple” situations that are analytically tractable because they are insightful and provide useful springboards for the study of more complicated scenarios. This tutorial which also includes key pointers to the literature should be helpful for junior and senior undergraduate students graduate students and researchers from mathematics physics and engineering who seek to study dynamical systems on networks but who may not have prior experience with graph theory or networks. Mason A. Porter is Professor of Nonlinear and Complex Systems at the Oxford Centre for Industrial and Applied Mathematics Mathematical Institute University of Oxford UK. He is also a member of the CABDyN Complexity Centre and a Tutorial Fe llow of Somerville College. James P. Gleeson is Professor of Industrial and Applied Mathematics and co Director of MACSI at the University of Limerick Ireland. Introduction: How Does Nontrivial Network Connectivity Affect Dynamical Processes on Networks A Few Basic Concepts Examples of Dynamical Systems General Considerations Software Implementation Dynamical Systems on Dynamical Networks Other Resources Conclusion Outlook and Open Problems Appendix.