The Rise of Islam

Wilken's ch. 30 is on Islam. Most of the chapter is just a summary of Muhammad's life and an introduction to Islam in the early years. Wilken also covers the early expansion of Islam through conquest, including the conquest of Jerusalem. 

Wilken mentions early on some pre-Islamic Arabic goddesses: Allat (wikipedia); al-Uzza (wikipedia); and Manat (wikipedia)

pre-Islamic Arab goddesses; Wikimedia Commons

See the Book of Idols (wikipedia) by the eighth-century Arab writer Hisham ibn al-Kalbi (wikipedia), available in English at archive.org.

The Byzantine Chronicler mentioned by Wilken (p. 288) is Theophanes the Confessor (c. 759–818, wikipedia), who continued the chronicle of George Syncellus, at the latter's request (according to Wikipedia). There is a translation of the Chronicle, by Cyril Mango and Roger Scott (Oxford, 1997), available in full at archive.org, or from Oxford for $450. The portion about Muhammad appears on p. 464, and Roger Pearse also excerpted the relevant portion (here). 

The Armenian chronicler mentioned by Wilken (p. 292), is Sebeos (wikipedia), whose chronicle was translated by R. W. Thomson (Liverpool, 1999), and which is also available in full at archive.org. The portion quoted by Wilken appears at p. 97. 

Wilken briefly describes the Battle of the Yarmuk (wikipedia) in August 636, a decisive Muslim victory over the Byzantine army that spelled the end of Roman/Byzantine rule in Syria after seven centuries. 

Jerusalem was besieged in 636/637 (wikipedia), and Sophronius, patriarch of Jerusalem, negotiated surrender with the caliph, Umar. 

The "Christian chronicler who wrote in Arabic in Egypt in the tenth century," quoted by Wilken (p. 293), is Eutychius of Alexandria (wikipedia). 

Wilken describes the place of Christians in this new society. 

To deal with the non-Muslim population the Arabs adopted a system similar to what had been in effect in the Persian Empire: the imposition of a tax on a segment of society. The Arab Muslims were considered privileged, and non-Muslims were required to pay a tribute, called jizyah [wikipedia], levied on males of military age, including Christians, Jews, Zoroastrians, and Samaritans, collectively known as the "people of protection") ahl al-dhimma in Arabic, or dhimmis). The basis for the legislation was found in a passage in the Qur'an: "Fight those who believe not in God and the last Day and do not forbid what God and his messenger have forbidden—such men as practice not the religion of truth, being of those who have been given the book—until they pay the tribute readily and have been humbled" (Qur'an 9:29). Christians were allowed to live in the lands that were formerly theirs and to follow their own laws on matters that concerned their religious life—on the condition that they submit to Muslim law in civl and criminal matters and pay the jizyah. The several Christian groups became societies within society, and int he early years they were able to carry on their affairs largely independent of the Muslim rulers. (Wilken pp. 294–95)

Wilken cites as  an interesting example Sarjun ibn Mansur (wikipedia), a Melkite Christian, who served as CFO of Syria during the early Umayyad Caliphate. His son was John of Damascus (wikipedia). But, as Wilken notes, soon enough Muslim society was not quite as happy to employ Christians in such high-ranking positions.