The Kagyu (bka' brgyud) School ("the Spotless Practice Lineage") traces its origins to the teachings of the Indian mystics Tilopa (988-1089 CE) and Naropa (1016-1100 CE), whose lineage was transmitted in Tibet by the great translator Marpa (1012-1097 CE).
Marpa's principal disciple was Milarepa (1052-1135 CE), arguably Tibet's best known religious poet and meditator. Amongst Milerapa's many students was Gampopa (1079-1153 CE), a great synthesizer, who can be recognized as the real founder of Kagyu as a distinct School of Tibetan Buddhism. Following Gampopa's teachings, there evolved the so-called "Four Major" and the "Eight Minor" lineages of the Kagyu School.
The head of the Kagyu school,more specifically of its Karma Kagyu tradition, is the Gyalwa Karmapa, whose appearance is said to have been predicted by the Buddha in the Samadhiraja Sutra (lit: Sermon regarding the Kings of Meditative Absorption). Currently there is a dispute regarding the identity of the 17th Karmapa (this dispute was predicted by the 12th Karmapa). Other prominent lamas (lit: Teachers) include the Shamarpa and T'ai Situpa.
The central teaching of this School is the doctrine of Mahamudra, or "the Great Seal", as elucidated by Gampopa in his various works. This doctrine focuses on four principal stages of meditative practice (the Four Yogas of Mahamudra), namely:
1- The development of single-pointedness of mind,
2- The transcendence of all conceptual elaboration,
3- The cultivation of the perspective that all phenomena are of a "single taste",
4- The fruition of the path, which is beyond any contrived acts of meditation.
It is through these four stages of development that the practitioner is said to attain the perfect realization of Mahamudra.