In the early Middle Ages, learning was limited to the Church. Only in Italy, lay literacy seems to have survived from the Roman age onwards. In the late 8th century, Charlemagne started a program to increase learning and literacy now known as the Carolingian Renaissance. In the late ninth century, the Anglo-Saxon king Alfred the Great followed this example. Both upsurges of literacy must be seen in a relative light: Although literacy did increase to a certain extent, all out literacy amongst the population remained severely limited. Some nobility would be educated in writing and Latin, but not all.
After these periods of learning, there was once more a decrease in the amount of books published, and so probably education of people. Learning once again increased from the 11th century onwards. It is estimated that in the early 12th century, about 70% of English and Norman nobility was literate. In Italy, an early 13th century chronicler of Florence estimated that about 90% of all male inhabitants of his city had received at least some primary education.
This increased literacy amongst the lay population caused an increase in lay literature, like Chivalric and Courtly poetry. The main centre of this type of literature was France, in particular the Provence. Italy soon took over with writers like Boccaccio.
Universities had been coming up since about the 10th century. The oldest University in Europe is at Bologna, (It claims to date from 1088, but this is a guess) were law was the main subject. Close followers were Paris (specialised in Theology), Oxford and Leuven.
The curriculum consisted of the Trivium (Grammar, Logic, Rhetoric) and the Quadrivium (Arithmetric, Geometry, Music (the art of harmony and the heavenly spheres, not nice tunes and, Astronomy). The Trivium was prmary education, the quadrivium secondary.
This is not half you want to know and not half I can tell, but I am out of time... Hope this is at least a start...