The Hagia Sophia was built just after the birth of the Roman Christian tradition, and came well before the advent of Renaissance oil paintings in churches. It was also built in the Middle East, and was influenced by the artistic traditions of the area. It therefore likely has mosaics on the inside, which are the cornerstone of Byzantine church art.

Image adapted from http://www.publicdomainpictures.net/hledej.php?hleda=hagia+sophia+5.

Islamic tradition bans the depiction of figures as inspiring idolatry; works depicting figures would be considered sacrilegious. When the church became a mosque, the mosaics were plastered over so that there were no faces in the new mosque, and there would only be Arabic script as decoration.

Image adapted from http://www.publicdomainpictures.net/hledej.php?hleda=hagia+sophia+5.

All of these are problems that have concerned and maddened builders since the construction of the building began, and all the problems are related to one other. The dome is very heavy, and when it's sitting on the foundation, it pushes the buttressing outward. The dome is so heavy in part because the brick to mortar ratio is 1:1, making the dense and heavy mortar far more weighty than it should be. 

Image adapted from http://www.publicdomainpictures.net/hledej.php?hleda=hagia+sophia+5.

The Hagia Sophia has been a Greek Orthodoxy church, a Roman Catholic Cathedral, a Mosque, and a museum. In fifteen hundred years of history, the building has seen influence from all over Europe. The minarets are Islamic, the mosaics on the interior are Byzantine, and the plan is Basilica, based on the Roman civic structures. What is has not ever seen the influence of, however, is the Church of England, which came about after the Hagia Sophia had already become a mosque.

Image adapted from http://www.publicdomainpictures.net/hledej.php?hleda=hagia+sophia+5.

Upon its completion, the Hagia Sophia was the largest cathedral in the world, and also contained the largest dome in the world. This dome was achieved through the use of fully-developed "pendentives," triangular elements of a sphere used as structural supports to allow a dome to be raised over a square room. The Hagia Sophia's architectural innovations were widely copied in Orthodox churches and Muslim mosques in successive centuries.

Tribunes are galleries above the inner aisle that open down into the nave. These housed overflow crowds in Medieval churches, such as San Clemente in Rome.

The drum of a building is the circular wall that supports a dome.

In sexpartite rib vaulting, each vault is divided into six sections by three ribs.

A pieta is a carved or painted artistic depiction of Mary holding her son Jesus in her arms after his crucifixion. When this depiction includes other people in the scene, it is referred to as the Lamentation.

A finial is a crowning ornament on a pinnacle, tower, or roof of a building.