The first monastery to house Tibetan monks was Samye (bsam yas), built in the late eighth century under the sponsorship of king Trisong Detsen (khri song sde btsan; 742-798). It was at Samye that the legendary debate between Kamalaśīla and the Chinese Ch'an monk Mohoyen took place, marking Tibet's inclination towards Indian textual study, as opposed to Chinese-influenced meditative practices.
The first major center of philosophical studies in Tibet was the monastery of Sangpu, founded in 1073. Sangpu developed a focus on translating Sanskrit texts and on the study of Dharmakīrti's epistemological treatises. It is here that such practices as debate, as well as the efforts to systematize the Indian texts, first entered the Tibetan scene. The tradition originating at Sangpu was so influential that it is sometimes pointed to as the beginning of Tibetan scholasticism.
Mindroling, Dorje Drag and Kathog
The oldest of the six great Nyingma monastic universities, called Kathog, was founded in the year 1159. Other great monastic universities were built beginning in the 15th century in central Tibet, including the preeminent Nyingma monastic educational institution, Mindroling (smin grol gling), founded in 1676 by the Rigzin Terdag Lingpa (rig 'dzin gter bdag gling pa), and Dorje Drag (rdo rje brag), founded in 1659. Unlike the later Gelug institutions, the Nyingma universities did not adopt a single standardized curricula. Rather, they tended to revolve around the study of a set of thirteen great texts, including Nagarjuna's Mulamadhyamakakarika (Treatise on the Middle Way) and Candrakirti's Madhyamakavatara (Introduction to the Middle Way).
While the Kagyü school was the first after the Nyingma to establish a monastery in Tibet - Reting was founded in 1056 CE - until the twentieth century these monasteries were not configured as large centers for textual study in a way that can be described as 'monastic universities.' With its divisions into multiple sub-sects and its many branch monasteries, the Kagyü lineage has tended to conduct its rigorous textual study on a smaller scale. However, an institution for scholarly study was founded in the mid-twentieth century in Pelpung (dpal spung) monastery in Kham, at the request of the Eleventh Tai Situ. Plans were under way to establish a similar center for study at the Karma Kagyü lineage's seat, Tsurphu Monastery, but were halted by the communist invasion of Tibet in 1959.
The Sakya school originated out of the lineage of the translator Drokmi (992-1072). The monastery of Sakya, from which the school takes its name, was founded in 1073. Initially, the Sakya center was a center for tantric practice open to monastics and lay students alike, and only gradually developed into a major scholastic center. It was largely under the influence of the great Sakya Pandita Kunga Gyaltsen (sa kya pandita kun dga' rgyal mtshan, 1182-1251) that Sakya Monastery emerged as a major scholastic institution.
Sera, Drepung and Ganden
Within the Gelug school tradition there are five central monasteries, the three largest of which are together known as the "Three Seats" (gdan sa sum). The earliest of these was Ganden (dga' ldan ), founded in 1409, and lending its name to the movement headed by Lama Tsongkhapa, whose followers were originally known as the Gandenpa, after the name of this first monastery. Drepung ('bras spungs), the second of the three to be founded, was established in 1416 by Lama Tsongkhapa's disciple Jamyang Chöje ('jam dbyangs chos rje). The third seat to be built was Sera (se rwa), founded by Tsongkhapa's disciple Jamchen Chöje ('jam chen chos rje) in 1419. Sera and Drepung are both located within three miles of Lhasa. These 'Three Seats' were the largest monastic universities in Tibet, and very possibly the largest in the world. Prior to 1959, Ganden housed 7,000 monks, Drepung more than 13,000, and Sera 10,000.
Students at these Gelug monastic universities undergo a rigorous 20-year degree program, culminating in the rank of Geshe (dge bshes). The curriculum of these universities is distinguished amongst Tibetan scholastic centers by several notable features. Most prominent is the crucial role given to formal debate. Before 1959, monks at the three seats would debate as many as eight hours a day. Students were required to pass annual examinations, and were further tested at the conclusion of their course of study in public debates. Another distinctive feature of this curriculum was the relatively small number of texts studied: during the course of the entire 20-year curriculum only five root texts are studied. http://www.maitripa.org/universities.html