The present volume is the first of two parts which constitute the proceedings of the 1986 Advanced Course on Petri Nets in Bad Honnef. It presents a number of central petri net models and their properties setting a firm formal basis for developing the theory of petri nets and for their adaption in a wide range of applications. These current issues of the "Advances in Petri Nets" present the most significant recent results in the application and theory of petri nets to the broad computer science community. They particularly address those who are: - interested in systems design and would like to learn to use petri nets, - familiar with subareas of the theory or the applications of nets and wish to become acquainted with the whole area, - interested in learning about recent results presented within a unified framework, - going to learn about successfully applying petri nets in various practical situations, - interested in the relationship of petri nets to other models of concurrent systems.