1. The Petri Net Model -- 1 Discrete event systems -- 2 Notation -- 3 Order theoretical preliminaries -- 4 Petri net definition -- 5 Petri nets as discrete event system models -- 6 Reachable sets -- 7 Graphical representation -- 8 Reachability via subsets of transitions -- 9 Other concurrency assumptions -- 10 A general Petri net definition -- 11 Notes and references -- 2. Supervisory Control -- 1 Control goal and architecture -- 2 Formal definition -- 3 Reachable sets under supervision -- 4 Maximally permissive control laws -- 5 Specific control sets -- 6 Linear inequalities as a legal set -- 7 Control design under the no concurrency assumption -- 8 Notes and references -- 3. Uncontrollable Events And Transitions -- 1 Introduction -- 2 Supervisory control laws -- 3 Specific concurrency and control assumptions -- 4 Maximally permissive control laws -- 5 Control design -- 6 The supremal controllable subset -- 7 Notes and references -- 4. Reduction Theorems -- 1 Intuition for A* -- 2 Invariance properties of the legal set -- 3 Sets of places and transitions -- 4 Reduction result for A* -- 5 Reduction of the control design -- 6 Structural and invariance properties of the legal set -- 7 Notes and references -- 5. Acyclic Petri Nets -- 1 Partitioning of the sets of places and transitions -- 2 Structure of the incidence matrices -- 3 Reachability in acyclic Petri nets -- 4 A reachability algorithm -- 5 Acyclic Petri nets free of choice places -- 6 Construction of the supremal controllable subset -- 7 Notes and references -- 6. Decomposition Of The Control Design -- 1 Introduction -- 2 Unions of legal sets -- 3 A uxiliary results -- 4 Proof of Theorem 6.1 -- 5 Discussion -- 6 Control design -- 7 Notes and references -- 7. Continuous Versus Discrete Events -- 1 Continuous Petri nets -- 2 A subset of the supremal controllable subset -- 3 Construction of the supremal controllable subset -- 4 No synchronising transitions in NAuc -- 5 No choice places in NAuc -- 6 A third class -- 7 Structure of A* -- 8 Notes and references -- 8. Structural Linear Algebraic Control Design -- 1 Unobservable events -- 2 Overview of the approach -- 3 Intersection of a linear halfspace with the first orthant -- 4 Candidate sets A?? -- 5 Maximal sets A?? -- 6 Reduction of controllers with disjunctions -- 7 A subset of the supremal controllable subset -- 8 Notes and references -- References.