Complex sentence: The Mongols had already conquered many Christian and Muslim nations in their advance across Asia, and after destroying the Muslim Abbasid and Ayyubid dynasties, for the next few generations fought the remaining Islamic power in the region, the Egyptian Mamluks.
Split into simpler sentences: The Mongols had already conquered many Christian and Muslim nations in their advance across Asia. After destroying the Muslim Abbasid and Ayyubid dynasties, for the next few generations the Mongols fought the remaining Islamic power in the region, the Egyptian Mamluks.