Barring the Qur'an and the Constitutional of Medina, it would be fair to say that all the other earliest sources for the rise of Islam and the Arab conquests were written by non-Muslims. As a result, there is a vast range of scholarship on this topic. I quoted most of the more well-known accounts in this thread and tried to synthesise the evidence from diverse Latin, Greek, and Syriac sources into a coherent narrative. More specifically, I have also tackled whether Christians viewed Islam as a heresy in this thread and discussed the cultural milieu into which Islam was born here - I essentially argued that Islam could not be separated from its late antique (and often Christian) context, which both shaped and was shaped by the portrayals of Islam in the sources.

For further reading, Robert Hoyland has studied these sources extensively in his excellent Seeing Islam As Others Saw It: A Survey and Evaluation of Christian, Jewish and Zoroastrian Writings on Early Islam (1997). The Syriac sources meanwhile have been recently translated by Michael Penn in his When Christians First Met Muslims A Sourcebook of the Earliest Syriac Writings on Islam (2015); a more analytical look at the same sources can be found in the companion volume, Envisioning Islam: Syriac Christians in the Early Muslim World (2015).