Can somebody please tell me about the conquest of Spain?

Actually, no. The Iberian Peninsula was not conquered by armies, but were converted to Islam voluntarily primarily because of the oppressive nature of the Roman Empire including the high taxes they levied to support their military adventures. There was growing resentment of the Romans among the alarmed unconquered as well as high level of rebellion among those conquered by the Romans, and what the Muslims offered was essentially a return to a republic form of government via the sharia arrangement.

It's wrong to call the Iberian Peninsula the "Califate of Cordoba" because it was, in fact, an Emirate...so it's correctly called the "Emirate of Cordoba". The north African coast was where the old empire of Carthage existed and was vanquished by the Romans, so there was no love for Romans lost there, as those sorts of grudges were maintained from generation to generation.

The Iberian Peninsula was previously occupied by primarily Celts, who regarded Rome as a threat and readily allied themselves with the Muslims, as did the usually separatist Basques in the north of that peninsula. The "division" into separate "small kingdoms" alleged in 1002 was just sharia law (local government on tribal basis) in action, but on the whole, the Iberian Peninsula was united under Baghdad rule until Genghis Khan invaded and razed Baghdad in the 13th century (1258 CE). Without imperial support forthcoming, the Franks thereafter succeeded in driving out both Muslims and Jews, the latter of which also prospered under the Islamic empire--thus was launched the infamous Inquisition.

There was a minor internal dispute in 778 when Charlemagne was approached by the Emir of Saragossa, soliciting a charge against the Cordoba government, but both were distracted by Saxon invasions--so not much came of that.

In 711 and 712 , Muslim armies of Arabs and Berbers from Africa took control of all the peninsula , except for the mountainous north where Christian kingdoms survived . For the next six centuries , Spain was divided between the Christians and the Muslims or Moors - a name derived from Mauri, a North African Berber people.

In 1002 the Caliphate of Cordoba split into many small kingdoms and the power of the Moors began to decline .

The Moors tolerance of race and religion that had characterised the early centuries of Muslim rule was replaced in the reconquered Christian kingdoms by religious and racial persecution .

The Moors were driven out of Granada , their last stronghold in 1492

The name Moor is derived from a Greek word (Mauros ) from the inhabitants of ancient Mauretania