The 13th volume of ToPNoC contains revised and extended versions of a selection of the best workshop papers presented at the 38th International Conference on Application and Theory of Petri Nets and Concurrency, Petri Nets 2017, and the 17th International Conference on Application of Concurrency to System Design, ACSD 2017. The 9 papers cover a diverse range of topics including model checking and system verification, refinement, and synthesis; foundational work on specific classes of Petri nets; and innovative applications of Petri nets and other models of concurrency. Application areas covered in this volume are: fault-tolerance, service composition, databases, communication protocols, business processes, and distributed systems. Thus, this volume gives a good overview of ongoing research on concurrent systems and Petri nets.