Geometry lies at the core of the architectural design process. It is omnipresent, from the initial form-finding stages, to novel manufacturing techniques, to the construction, and to post occupancy monitoring. But the role of geometry in architecture and engineering is also continuously evolving. Geometry increasingly plays a role in modeling environments and processing sensing information. Modern geometric computing provides a variety of tools for the efficient design, analysis, and manufacturing of complex shapes. Besides descriptive geometry controlling form, algorithmic processes play a crucial role in integrating disciplinary input. On the one hand this opens up new horizons for architecture. On the other hand, the architectural context also poses new problems to geometry. Around these problems the research area of architectural geometry has emerged. It is located at the common border of architecture with applied geometry, computational design, mathematics, and manufacturing.