Kagyu

The Kagyu school, also transliterated as Kagyü, or Kagyud, which translates to "Oral Lineage" or "Whispered Transmission" school, is one of the four major schools of Tibetan Buddhism. The Kagyu lineages trace themselves back to the 11th century Indian Mahasiddhas Naropa, Maitripa and the yogini Niguma, via their student Marpa Lotsawa, who brought their teachings to Tibet. Marpa's student Milarepa was also an influential poet and teacher.
The Tibetan Kagyu tradition gave rise to a large number of independent sub-schools and lineages. The principal Kagyu lineages existing today as independent schools are those which stem from Milarepa's disciple, Gampopa, a monk who merged the Kagyu lineage with the Kadam tradition. The Kagyu schools which survive as independent institutions are mainly the Karma Kagyu, Drikung Kagyu, Drukpa Lineage and the Taklung Kagyu. The Karma Kagyu school is the largest of the sub-schools, and is headed by the Karmapa. Other lineages of Kagyu teachings, such as the Shangpa Kagyu, are preserved in other schools.
The main teachings of the Kagyus include Mahamudra and the Six Dharmas of Naropa.

Nomenclature, orthography and etymology

Strictly speaking, the term bka' brgyud "oral lineage", "precept transmission" applies to any line of transmission of an esoteric teaching from teacher to disciple. There are references to the "Atiśa kagyu" for the Kadam or to "Jonang kagyu" for the Jonang and "Ganden kagyu" for the Gelug sects. Today, however, the term Kagyu almost always refers to the Dagpo Kagyu and, less often, to the Shangpa Kagyu.

"Kagyu" and "Kargyu"

In his 1970 article Golden Rosaries of the Bka' brgyud schools, E. Gene Smith discusses the two forms of the name, and :
One source indicates:

Origins

Kagyu begins in Tibet with Marpa Lotsawa a Tibetan householder who trained as a translator with lotsawa Drogmi Shākya Yeshe, and then traveled three times to India and four times to Nepal in search of religious teachings. His principal gurus were the siddhas Nāropa – from whom he received the "close lineage" of mahāmudrā and tantric teachings, and Maitrīpāda – from whom he received the "distant lineage" of mahāmudrā.
Together Marpa, Milarepa and Gampopa are known as "Mar-Mi-Dag Sum" and together these three are considered the founders of the Kagyu school of Buddhism in Tibet.

Indian origins

Marpa's guru Nāropa was the principal disciple of Tilopa from East Bengal. From his own teachers Tilopa received the Four Lineages of Instructions, which he passed on to Nāropa who codified them into what became known as the Six Doctrines or Six Dharmas of Naropa. These instructions consist a combination of the completion stage practices of different Buddhist highest yoga tantras, which use the energy-winds, energy-channels and energy-drops of the subtle vajra-body in order to achieve the four types of bliss, the clear-light mind and realize the state of Mahāmudrā.
The Mahāmudrā lineage of Tilopa and Nāropa is called the "direct lineage" or "close lineage" as it is said that Tilopa received this Mahāmudrā realisation directly from the Dharmakāya Buddha Vajradhara and this was transmitted only through Nāropa to Marpa.
The "distant lineage" of Mahāmudrā is said to have come from the Buddha in the form of Vajradara through incarnations of the bodhisattvas Avalokiteśvara and Mañjuśrī to Saraha, then from him through Nagarjuna, Shavaripa, and Maitripada to Marpa. The Mahāmudrā teachings from Saraha that Maitripa transmitted to Marpa include the "Essence Mahāmudrā" where Mahāmudrā is introduced directly without relying on philosophical reasoning or yogic practices.
According to some accounts, on his third journey to India Marpa also met Atiśa who later came to Tibet and helped found the Kadam lineage

Marpa and his successors (Marpa Kagyu)

Marpa established his "seat" at Drowolung in Lhodrak in southern Tibet just north of Bhutan. Marpa married the Lady Dagmema, and took eight other concubines as mudras. Collectively they embodied the main consort and eight wisdom dakini in the mandala of his Yidam, Hevajra. Marpa wanted to entrust the transmission lineage to his oldest son, Darma Dode, following the usual Tibetan practice of the time to transmit of lineages of esoteric teachings via hereditary lineage, but his son died at an early age and consequently he passed his main lineage on through Milarepa. Darma Dode's incarnation as Indian master Tiphupa became important for the future development of Kagyu in Tibet.
Marpa's four most outstanding students were known as the "Four Great Pillars" :

Milarepa, born in Gungthang province of western Tibet, the most celebrated and accomplished of Tibet's yogis, who achieved the ultimate goal of enlightenment in one lifetime became the holder of Marpa's meditation or practice lineage. Among Milarepa's many students were Gampopa, a great scholar, and the great yogi Rechung Dorje Drakpa , also known as Rechungpa
Ngok Choku Dorje – was the principal recipient of Marpa's explanatory lineages and particularly important in Marpa's transmission of the Hevajra Tantra. Ngok Choku Dorje founded the Langmalung temple in the Tang valley of Bumthang district, Bhutan—which stands today. The Ngok branch of the Marpa Kagyu was an independent lineage carried on by his descendants at least up to the time of the Second Drukchen Gyalwang Kunga Paljor who received this transmission, and 1476 when Go Lotsawa composed the Blue Annals.
Tshurton Wangi Dorje – was the principal recipient of Marpa's transmission of the teachings of the Guhyasamāja Tantra. Tshurton's lineage eventually merged with the Shalu Monastery tradition and subsequently passed this down to the Gelug founder Je Tsongkhapa, who wrote extensive commentaries on the Guhyasamāja Tantra.
Meton Tsonpo

Other important students of Marpa include:

Marpa Dowa Chokyi Wangchuck.
Marpa Goleg who along with Tshurton Wangdor received the Guhyasamāja Tantra.
Barang Bawacen – who received lineage of the explanatory teachings of the Mahāmāyā Tantra.

Jamgon Kongtrul collected the initiations and sadhanas of surviving transmissions of Marpa's teachings together in the collection known as the .

Gampopa

Gampopa, who was a Kadampa monk, is an influential figure in the history of the Kagyu tradition. He combined the monastic tradition and the stages of the path teachings of the Kadam order with teaching and practice of the Mahāmudrā and the Six Yogas of Naropa he received from Milarepa synthesizing them into one lineage. This monastic tradition came to be known as Dagpo Kagyu—the main lineage of the Kagyu tradition passed down via Naropa as we know it today. The other main lineage of the Kagyu is the Shangpa Kagyu, passed down via Niguma. Gampopa's main contribution was the establishment of a celibate and cenobitic monastic Kagyu order. This was in sharp contrast to the tradition of Marpa and Milarepa which mainly consisted of non-monastic householder or hermit yogis practicing in solitary locations or hermitages. According to Tibetologist John Powers, Marpa "saw the monastic life as appropriate only for people of limited capacities." Gampopa on the other hand, founded Daklha Gampo Monastery and thus allowed the Kagyu teachings to have established training centers and study curricula in a structured monastic setting which was well suited to the preservation of tradition.
Most of the major Kagyu lineages in existence today can be traced through Gampopa.
Following Gampopa's teachings, there evolved the so-called "Four Major and Eight Minor" lineages of the Dagpo Kagyu School. This phrase is descriptive of the generation or order in which the schools were founded, not of their importance.

Dagpo Kagyu lineages

The principle Dagpo Kagyu lineages that exist today as organized schools are the Karma Kagyu, Drikung Kagyu and the Drukpa Lineage. For the most part, the teachings and main esoteric transmissions of the other Dagpo Kagyu lineages have been absorbed into one of these three independent schools.
Historically, there were twelve main sub schools of the Dagpo Kagyu derived from Gampopa and his disciples. Four primary branches stemmed from direct disciples of Gampopa and his nephew; and eight secondary branches derived from Gampopa's disciple Phagmo Drupa. Several of these Kagyu traditions in turn developed their own branches or sub-schools.
The terminology "primary and secondary" for the Kagyu schools can only be traced back as far as Kongtrul's and other's writings. The Tibetan terminology "che chung", literally "large small," does not reflect the size or influence of the schools, as for instance the Drikung school was in the 13th century probably the largest and most influential of them, although it is, according to Kongtrul, "secondary".Or it can be taken as early and later schools.

Four primary branches of the Dagpo Kagyu

Karma Kamtsang (Karma Kagyu)

The Drubgyu Karma Kamtsang, often known simply as Karma Kagyu, was founded by one of Gampopa's main disciples Düsum Khyenpa, 1st Karmapa Lama . The figure of Karma Pakshi, a student of one of Düsum Khyenpa's main disciples, was actually the first person recognized as a "Karmapa", i.e. a reincarnation of Düsum Khyenpa.
Rangjung Dorje, 3rd Karmapa Lama, was an important figure because he received and preserved Dzogchen teachings from Rigdzin Kumaradza and taught this along with Kagyu Mahamudra. He also influenced Dolpopa Sherab Gyaltsen, the founder of the Jonang school who systematized the shentong teachings.
The Karmapas continue to be the heads of the Karma Kagyu order today and remain very influential figures. According to Reginald Ray:

Although in the diaspora the sixteenth Karmapa was considered the “head” of the Kagyu lineage, in Tibet the situation was more decentralized. In spite of the titular role of the Karmapa, even in exile the various surviving Kagyu subschools maintain a high degree of independence and autonomy.

Following the death of Rangjung Rigpe Dorje, 16th Karmapa in 1981, followers came to disagree over the identity of his successor. The disagreement of who holds the current title of Karmapa is an ongoing controversy termed the "Karmapa controversy".