Short answers, pulled from the story.
The Neolithic village of Khirokitia on Cyprus provides the first evidence for communities with curved brick architecture and beehive-shaped corbel domes around 3000 BCE. These structures used unfired mud-bricks to create circular buildings that supported an upper floor.
Romans developed barrel cross and dome vaults using concrete mixed with pozzolana mortar found near Rome. This volcanic deposit hardened the concrete to become as solid as rock when it set, allowing for massive structures like the Piscina Mirabilis reservoir at Baiae.
The first introduction of the pointed arch rib took place at Cefalù Cathedral before the abbey of Saint-Denis. It was extended to the square bay of the porch at the church at Vezelay in 1140.
Justinian instructed his architect to design the Church of the Holy Wisdom Hagia Sophia at Constantinople with a pendentive that carried the dome. The pendentive rested on four great arches while immense buttresses traversed the aisles to counteract the thrust.
Gol Gumbaz is the tomb of Muhammad Adil Shah II built between 1626 and 1660. Its distinctive Karbandi ribs intersect one another to reduce the central opening to 3 meters in diameter.