The Sera and Drepung monasteries are two of the 'great three' Gelukpa university monasteries of Tibet.
Sera Monastery is located in the foot hills 2 kilometers north of Lhasa. The origin of the name 'Sera' is attributed to a fact that the site where the monastery was built was surrounded by wild roses (se ra in the Tibetan language) in bloom. The Sera Monastery, as a complex of structures with the Great Assembly Hall and three colleges, was founded in 1419.
The Sera Monastery in Tibet, and its counterpart in Mysore India, are the best locations to witness the "Monk Debates" on the teachings of Buddha and the philosophy of Buddhism. Sera Monastery developed over the centuries as a renowned place of scholarly learning, training hundreds of scholars.
Drepung Monastery (literally "Rice Heap" monastery) is located at the foot of Mount Gephel (Gambo Utse), five kilometers from the western suburbs of Lhasa. Drepung is the largest of all Tibetan monasteries.
Drepung was founded in 1416 and is the principal seat of the Gelugpa school of Buddhism. The Ganden Podang in Drepung was the residence of the Dalai Lamas until the Great Fifth Dalai Lama constructed the Potala Palace. Drepung was known for the high standards of its academic study, and was called the Nalanda of Tibet, a reference to the great Buddhist monastic university of India. (Information based on Wikipedia articles)