what events shaped the rise of muslim arab empires and the eventual transfer of power to the selijuk turks?

The rise of the Muslim Arab empires was due to the emergence of the Islam as a religion. This religion managed to unify the Arab tribes, and they went into a military campaigns to spread the religion and conquer new territories. Because the surrounding empires were not in great shape and significantly weakened because of multiple reasons, the Muslim Arab empires managed to gain control of lots of new areas with relative ease.

When the Mongols started expanding under the leadership of Genghis Khan, one of the Muslim empires, Quaresmia, made a huge mistake with provoking Genghis Khan with the brutal decapitating of his messengers, and he let his hordes which destroyed the Muslim empires and took their territory, as well as ruining big portion of the cities and killing millions of people.

Once the Mongol Empire started to fall apart, the Seljuk Turks used the opportunity and the open space, and they went onto a military campaign in which they managed to create an empire, but it was not long lasting.