If one were inclined to rank the most important battles in world history, the Battle of Yarmouk probably should be pretty high on the list. It eliminated, over the course of one 6-day battle, almost the entirety of the Byzantine military south of the Taurus Mountains, leaving Syria and the rest of the Levant (with Egypt waiting beyond that, and then the rest of North Africa) open to Arab conquest. Along with the Battle of Qadisiyah, which was fought in November and essentially destroyed the Sasanian (Persian) Empire, Yarmouk overturned the political situation in the Middle East and opened the way for Islam to emerge from the Arabian peninsula and spread into the wider world. I hope we can agree that was a pretty momentous development.
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The Foreign Exchanges Companion 
in your text you mention some sources could you please tel me what the sources are? 🙂
Baladhuri’s Kitab Futuh al Buldan, Tabari, al-Waqidi, Theophanes, lots more beyond that.