Greetings, McDread - haven't seen you in a while.
An important aspect about the Islamic presence in Iberia is its relationship with the rest of the Islamic world. Not long after Abd al-Rahman managed to subjugate most of Iberia in the mid-8th century he established Ummayad rule there, at a time when the Ummayads had just been violently booted from power elsewhere. Al-Rahman himself had fled from Syria when the Abbasid caliphate took over. Islamic Iberia was very isolated politically from the rest of the Moslem world, and indeed Cordoba flourished at a time when the Moslem learning centers to the east were in severe decline, being suppressed by clerics who were alarmed by scholasticism and subordinated it to faith. Only Iberia held out as a major learning center in the Islamic world centuries after Baghdad's study centers had fallen silent. The Moorish Moslem state was unique in the Islamic world.
An excellent book I recommend on this subject is Bernard Lewis' c. 1982 book,
The Moslem Discovery of Europe, which explores European-Islamic relations through history from the Moslems' perspective.
The Islamic period of Spain's (and Portugal's) history is a relatively happy one, certainly for the most part a prosperous one. In its later years the single city of Cordoba (as a Moslem city) had more libraries and schools than all of Christian Europe combined. Cordoba in this same period was something like the 2nd largest city in the world, second only to the Chinese capital at the time; no city in Christian Europe could begin to compare to Cordoba's population size. It also served as an important cultural meeting place for three cultures (Moslem, Christian, Jewish) to interact and exchange technologies and philosophies. The great mosque in Cordoba was built on the ruins of a Roman temple, an apt analogy for how all great civilizations build their greatness by borrowing heavily from neighboring civilizations, past and present. There is another great book by Franz Rosenthal,
The Classical Heritage in Islam, that explores how early Moslem scholars studied and expanded on old Greek and Roman texts they found, and what impact that had on Islamic civilization. And of course, as others have already mentioned Europe itself re-discovered much of its Classical heritage through the Moslems and Sephardic Jews. Some of the basic elements that fueled the Renaissance in Italy in the 13th and 14th centuries were born of Classical texts re-discovered from the Moslems, such as Aristotle, etc.
The Christian and Islamic civilizations have had a long and mostly mutually-hostile history but nonetheless there has been an amazing level of cultural exchange and impact between the two that has (mostly) benefitted both, despite their animosity. Islamic Iberia was a crucial component in that exchange.
Side note: The modern Moslem immigrants who perpetrated the recent bombing of the train line in Madrid claimed to want to revive the old Islamic state in Spain but I strongly suspect that were they transported back to Cordoba in its Moslem golden years, they would find themselves arrested and in deep trouble; Islamic Iberia did not suffer radicals or fanatics, preferring to emphasize prosperity and justice instead. These fundamentalist Moslems want an Taliban-style Islamic state, not an Ummayad-style.
Interesting
link here on Moorish Iberia.
