These Transactions publish archival papers in the broad area of Petri nets and other models of concurrency, ranging from theoretical work to tool support and industrial applications. ToPNoC issues are published as LNCS volumes, and hence are widely distributed and indexed. This Journal has its own Editorial Board which selects papers based on a rigorous two-stage refereeing process. ToPNoC contains: Revised versions of a selection of the best papers from workshops and tutorials at the annual Petri Net conferences Special sections/issues within particular subareas (similar to those published in the Advances in Petri Nets series) Other papers invited for publication in ToPNoC Papers submitted directly to ToPNoC by their authors The 15th volume of ToPNoC contains revised and extended versions of a selection of the best workshop and tutorial papers presented at the 40th International Conference on Application and Theory of Petri Nets and Concurrency, Petri Nets 2019, and the 19th International Conference on Application of Concurrency to System Design, ACSD 2019. The 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: process mining, verification, formal semantics, communication protocols, business processes, distributed systems, and net synthesis. Thus, this volume gives a good overview of ongoing research on concurrent systems and Petri nets.