What church combines the intricacies of greek theology, the ambitious architectural scale of rome, the vaulting tradition of the mesopotamia, and the mysticism of eastern christianity in order to create a monument that is the summation of antiquity and the triumph of christianity?

Hagia Sophia or Church of the Holy Wisdom

Explanation:

Your question cites Fred S. Kleiner's book Gardner's Art through the Ages: A Global History, Volume I

Hagia Sophia was a Greek Orthodox Christian patriarchal cathedral and now it is a museum. It's located in Istambul and was a Roman Catholic cathedral under the Latin Empire, Swiss-Italian architect brothers Gaspare and Giuseppe Fossati consolidated domes and vaults in the Renovation of 1847.

To say that it's " the summation of antiquity and the triumph of Christianity" is a Fred S. Kleiner's opinion due to in November 2013 Turkish Muslim people are demanding Hagia Sophia to be converted into a mosque again.