How was Learning preserved during Medieval time?

The short answer is that the Church was most important in the preservation of learning, but there were others involved.

In Western Europe, learning was preserved primarily by the Catholic Church, which was the most important source of education through the Early Middle Ages. There were state run schools, and these opened surprisingly early; Northumbria opened the Beverley Grammar School in 700 AD, and it is still operating today in Yorkshire. There were private schools of different kinds, and there were tutors.

Universities opened in the West in the 11th and 12th centuries when schools of higher education were formally chartered. Some of these were Church run, but others were state supported and still others were run independently of both Church and state.

In the East Roman Empire, a system of state supported primary education was opened in 425 AD, and it remained open through the rest of the Middle Ages, until the fall of Constantinople in 1453. The schools that eventually became the University of Constantinople were also opened in 425, and the Byzantine Empire also ran other Universities.

Aside from schools, books were copied, and their contents were thus preserved. The business of copying manuscripts was usually done by the Church, but there were some books that were copied privately. The great medieval libraries all depended on copied manuscripts, as the originals did not survive all that long.

Please see the links below.