One way to understand Islam is as a convergence of Jewish elements and Christian elements into a third synthesis.
Aside from a few stories about Jesus and Mary –including a hugely mistaken idea that she is the Third in the Trinity– the primary Christian contribution to Mohammed’s religion is its universal missionary horizon and assertion of finality: that Islam is to be propagated all over the earth as the faith of the Last Prophet. This is not a minor matter, for without it, Islam would have confined itself to Arabia.
But what is striking to a Christian reader of the Koran, to say nothing of the Hadith, is how much like Rabbinic Judaism it sounds, that is, how obsessed it is with legalities of all kinds. Although Christianity has its canon law about ritual, fasting, marriage, etc. that is a minor part of its focus compared to vast outpouring of energy on doctrine.
I have sometimes described Islam as the religion of a Hasidic Jew, but with a gun, a bad attitude and an imperialist agenda.
The Muslim laws about the treatment of captured women, about conversion and the treatment of conquered peoples, about modes of war, etc are astonishingly reminiscent of the Rabbinic laws based on the Torah, especially in Moses Maimonides’ classic and authoritative work, Mishneh Torah.
I am not claiming that Maimonides had an influence on Islam, since Mohammed’s religion is generally believed* to have arisen in 7th century Arabia and Maimonides lived in 13th century North Africa.
But Mishneh Torah is not at all outside the longstanding tradition of Talmudic Judaism dating from early post-Temple times and Mohammed was certainly engaged not only with Arab Christians but Arab Jews while he was constructing his new faith.
It is also not accidental that just as Judaism really owes more to the Talmudic interpretations of the Pentateuch than to the text itself, so Islam is defined more by the Shariah law based on the Hadith than by the relatively short Koran itself. Both are theocratic religions of sacred law codes.
*Some contemporary scholars are starting to question some quite basic elements of the received Muslim narrative.