1 Introduction.- 1.1 Why is Mathematics Useful?.- 1.2 Formal Methods in Software Development.- 1.3 Formal Methods and Object-orientation.- 1.4 Z++.- 1.5 VDM++.- 1.6 Adding Formality to Diagrammatic Methods.- 1.7 Problems in Object-oriented Development.- 2 The Software Development Process.- 2.1 Formal Object-oriented Development.- 2.2 Example Development: Shapes and Points.- 2.3 The Layered Development Paradigm.- 2.4 Development Example in VDM++.- 3 From Analysis to Formal Specification.- 3.1 Formalisation of Object Models.- 3.2 Aggregation.- 3.3 Alternative Approaches.- 3.4 Formalisation of Dynamic Models.- 3.5 The Booch Method.- 3.6 Specification Construction Principles.- 3.7 Animation.- 4 Specification Notations and Techniques.- 4.1 Attributes and Data Structures.- 4.2 Operations.- 4.3 Inheritance.- 4.4 Subtyping.- 4.5 Class Composition.- 4.6 Object Identity.- 4.7 Dynamic Behaviour.- 4.8 Complex Data Types.- 4.9 VDM++.- 5 Design and Refinement.- 5.1 Design Approaches.- 5.2 Refinement.- 5.3 Subtyping, Composition and Refinement.- 5.4 VDM++.- 6 Proof Methods and Techniques.- 6.1 Safety Reasoning - Monitor and Gate.- 6.2 Liveness Reasoning - Dining Philosophers.- 6.3 Internal Consistency Proofs.- 6.4 Refinement and Subtyping Proofs.- 6.5 Object Identity.- 6.6 Reasoning About Concurrent Object Execution.- 6.7 Synchronisation Refinement Proofs.- 6.8 General Refinement Proof Techniques.- 7 Concurrent and Real-time Behaviour.- 7.1 Extended Harel Statecharts.- 7.2 Specifying Reactive System Properties.- 8 Implementation and Code Generation.- 8.1 Translation into Procedural Languages.- 8.2 Introducing Concurrency in Implementations.- 8.3 Implementation Case Study: Personnel System.- 8.4 Testing.- 9 Case Studies.- 9.1 Invoice System.- 9.2 Expedited Data Queue.- 9.3 FireControl.- 9.4 Specification of Reactive Systems.- 9.5 Mine Pump Control.- A.1 Mathematical Notation.- A.2 Z Notation.- B.4 The Semantics of Procedural Statements.- B.5 Tool Support.- C Exercise Answers.- D Task Analysis.