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Kagyü (bkaʾ.brgyud, ‘oral transmission’). One of the four principal schools of Tibetan Buddhism, taking its name from the mode of transmission of its teachings before their proper systematization by Gampopa (1079–1153). To it, or to some of its sub-divisions, the name ‘Red Hats’ is often incorrectly given in the W. (for the use of that name, see RED HATS). Like the Nyingma, the Kagyü have a strong identification with the Indian siddha tradition, out of which they recognize two lineages culminating in Marpa (1012–97). From Nāropa, Marpa inherited the ‘Six Doctrines of Nāropa’, Tantric practices of mastery over self and phenomena which are now recognized by all schools, and which constitute the heart of a Kagyü lama's training. From Maitrīpa, Marpa inherited the philosophical doctrine of Mahāmudrā, in which the progression and culmination of the spiritual path are seen as the expression of a procreative śūnyatā, in which bliss, luminosity, and wisdom are seen to coincide.

From Marpa, the philosophy of Mahāmudrā and the practices of Nāropa passed to Milarepa, and from Milarepa to Gampopa, who had also studied in the Kadam tradition. It is only with Gampopa that one can begin to talk of a Kagyü ‘school’, and this immediately split into four subschools, the Tshal, Baram, Karma, and Druk. Today there are many Kagyü subschools, the two most important of which are the Druk (ʾbrug) Kagyü, founded by Yeshe Dorje (1161–1211), which became the dominant tradition in Bhutan, even giving its name to that country, and the Karma Kagyü, established by Düsum Chempa (1110–93), the first Gyalwa Karmapa hierarch, and which is generally today the dominant Kagyü school.

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