The single most significant fact about the Muslim empire is that, by around 725, it linked lands from the Atlantic to the Indian Ocean. This was the widest strip around the Equator that any empire had yet united. Most of the advances in science, mathematics, and technology that we remember as being from “the Muslims” came from this fact: that they ruled lands that had never been connected before.
During the late 600s, the Umayyad Caliphs had unified North Africa. It began with capturing Byzantine cities like Alexandria and Tunis, but it included subduing and converting the Berber and other nomadic tribes. Muslim historians sourly note that “bandits” were happy to do a surface conversion in order to join the winning army and get some plunder from the wealthy, previously off-limits, cities. North African nomad tribes became the backbone of Muslim military ferocity.
A North African general, Tariq ibn Ziyad, crossed the Straits of Gibraltar in 711. The Roman province of Hispania was loosely ruled by Visigoths, but the kingdoms were weak. The Visigoth aristocrats may have been the most arrogant nobles of all the German tribes. They had never really integrated with the remaining Roman, Jewish and Iberian people they were ruling, nor had they done anything to gain their loyalty. Although the nobles were brave fighters, they were no match for the sheer size of Tariq ibn Ziyad’s army. Conquest was rapid; the Visigoths pulled back into the foothills of the Pyrenees and the northern coast of the Atlantic. A line of small northern Christian kingdoms carried on Visigothic culture.
The peninsula was Muslim from Atlantic to Mediterranean, including the islands, and shortly it branched into modern France. France and Spain, so neatly divided on modern maps, have a large zone of blended and independent language and culture. Their Christians were Arian (and later Cathar). Muslim rule extended over this zone, as far as Narbonne and Marseille. They were defeated by the Duke of Aquitaine at Toulouse in 721, and for about ten years they consolidated power in Spain and waited.
Al-Andalus was just a province of the Umayyad Caliph’s empire. The caliph appointed governors. Andalusia only became independent after 750, with the next dynastic split. In this early period, its cities had not changed much, and the main point of the province was to produce tribute for Damascus. Many Jews, who were vastly more literate than the Spanish Romans, became part of Muslim city governments. The peasants continued to farm as they had done under every other occupation. The tax structure, of course, gave them strong incentives to declare themselves Muslim within a generation or two.