This document discusses different types of domes and vaults used in architecture. It defines a dome as a rounded vault resembling half of a sphere, which can be supported by columns transitioning to the dome. The main types of domes discussed are geodesic, hemispherical, umbrella, onion, and oval domes. Geodesic domes use a network of triangles to create a self-bracing structure. Vaults are ceilings built on arch principles, with common types being barrel, groin, rib, and fan vaults. Barrel vaults are semi-circular, while groin vaults are formed by intersecting barrel vaults. Rib vaults use reinforcing ribs.