This text explores the developments in geometric and product modelling, and their applications. In particular, it looks at the means by which product geometry emerges from the conceptual stages of design, and the use of geometric reasoning for applications downstream of design, including manufacture and assembly. Much existing design research is either totally geometry based or totally non-geometric, and the interface between the two areas is of great interest to industry, as well as being crucial for the successful development of integrated systems for design and manufacture. This interface is currently not well understood and the book attempts to make a contribution to its understanding. The following areas are amongst those addressed: computer-aided design and manufacture of mechanical products; computer integration of design and manufacturing; computational geometry; conceptual design and engineering tolerances; and assembly design and planning.