I quoted pretty much all the contemporary mentions of Muhammad here, let me know if you have any questions!

Edit: Sounds like there are a lot of follow-up questions to this, so I might as well link my answers explaining the success of the Arab Conquests, early Christian responses to Islam and how the Arabs conquered Egypt/North Africa :)

If In the Shadow of the Sword by Tom Holland is to believed, contemporary accounts of Mohammed are very rare indeed. Most accounts talk about a prominent leader in the area contested between the Roman Empire and Persia (that is the Near East and not Arabia proper).