Next generation manufacturing companies have to become highly responsive in order to succeed in an ever more rapidly changing global market. The ability to effectively develop and adapt their assembly facilities (systems) to changing requirements on demand plays a crucial role in achieving high responsiveness since the assembly process has to deal with the full inherent complexity of increasingly mass-customised products. This work was motivated by the current lack of a holistic assembly system design theory that would enable design environments to address the need for rapid system development and adaptation. The challenge is to create a common environment where domain experts can effectively collaborate while taking advantage of the best practices of their diverse domains. This thesis investigates how a domain ontology can help to overcome those challenges. The approach is taking advantage of the higher levels of standardisation inherent in the modular assembly system paradigm which is considered to be one of the fundamental enabling factors to achieve a high level of adaptation. A new ontology framework has been developed to support the design and adaptation of modular assembly systems (ONTOMAS). The ONTOMAS framework is based on engineering ontology principles structuring the domain using formalisms for aggregation, topology, taxonomies, and system theory principles. A number of design patterns have been identified and formalised to support key design decision-making tasks during the design of modular assembly systems. Furthermore, the function-behaviour-structure paradigm has been applied to capture the characteristics of modular assembly equipment at different levels of abstraction that reflect the specific needs of the engineering design process. The proposed ONTOMAS framework provides a sound foundation for computer based support tools to reduce the assembly system design effort and time while maintaining a high level of quality. An integrated design framework for the requirements driven specification of assembly processes and configuration of modular assembly system has been developed. The design approach applies the new formalisms of ONTOMAS to support the design decision-making activities. The developed ONTOMAS framework has been applied in several industrial and synthetic use cases to verify its applicability and appropriateness. Furthermore, the new ontology and design framework have been used as foundation for the development of a prototype collaborative design environment which allows different domain experts to participate in the design of modular assembly systems.