The Kagyu (or Kagyupa)  school is one of the four main schools or lineages of Tibetan Buddhism.

History and Branches of the Kagyu Tradition
The Kagyu teachings originated with the Indian mahasiddhas Tilopa and his student Naropa. The Kagyu school was founded in Tibet by Naropas follower Marpa Lowatsawa. Gampopa was the first monk of the Kagyu school. Gampopa's own followers founded many monasteries which resulted in several sub-schools or branches being established. At one time there were more than twelve different branches. Today there are four separate Kagyu sub-schools:

 The Karma Kagyu. This school was started by one of Gampopa’s main students, Karmapa Düsum Khyenpa (1110–1193). The head lamas of this lineage are the successive Karmapas. Followers of this school believe they are all incarnations or Tulkus of the first Karmapa Düsum Khyenpa.
 The Drikung Kagyu. This school was started in 1179 by Kyobpa Jigten Sumgön. The Drikung Kagyu is headed by two lamas known as Drikung Chetsang and Drikung Chungtsang.
 The Drukpa Kagyu. This school was started by the saint Tsangpa Gyare (1161–1211). Today there are two main branches:
 The Northern Drukpa Kagyu or Drukpa lineage of Tibet. This school is headed by a lama known as the Gyalwang Drukchen Rinpoche who followers believe is an incarnation of Tsangpa Gyare.
 The Southern Drukpa Kagyu of Bhutan. This school was started there by Shabdrung Ngawang Namgyal (1594–1651). It is the established sect of Buddhism in Bhutan and is headed by a lama called the Je Khenpo. 

The teachings of each of these schools have come down through different successions of masters since the time of Gampopa. However the teachings of all these Kagyu schools is essentially the same.

Teachings
The Kagyu school generally emphasises faith in the spiritual teacher or Lama and meditation practice over study. They teach that without this faith it is impossible to achieve the benefits and realization of meditation. However some basic study is also important. One of the most important books of this tradition is The Jewel Ornament of Liberation which was written by Gampopa. This book covers all the main teachings of Mahayana Buddhism in a step-by-step manner. In particular it teaches 
 how all living beings have an enlightened Buddha nature.
 the importance of relying on a spiritual teacher to realise this Buddha nature.
 how to contemplate on the golden opportunity of the brief human birth which we have.
 how to contemplate the faults or suffering of worldly cyclic existence.
 how to contemplate cause and effect of our actions.
 how to develop loving-kindness and compassion.
 about going for refuge in the Buddha, his teachings and the community of saints.
 about the importance of taking and maintaining Buddhist precepts.
 how to develop an enlightened attitude or ordinary and extraordinary compassion.
 how to practice the "six perfections" of generosity, moral ethics, patience, perseverance, concentration, and awareness.
 a description of the ten stages of realisation which are the result of these practices.
 a description of the state of complete Buddhahood or awakened enlightenment which is the final goal. 

The biographies and spiritual poems or songs of Kagyu saints, in particular the Life of Milarepa and the 100,000 Songs of Milarepa, are also widely read books of this tradition.

Advanced Meditation Practice
The  special advanced meditation practices of the Kagyu tradition consist of two main teachings:
 the six yogas or six doctrines of Naropa
 the Mahamudra or Great Seal teachings

The six yogas of Naropa involve complicated visualisation combined with yoga and breathing exercises. These practices are generally only done by monks and nuns who remain in strict seclusion for at least three years. They are called the six yogas or six doctrines of Naropa as they were originally taught by Naropa and consist of six main practices.    

The Mahamudra meditation teachings are meditations of concentration and awareness which allow the practitioner to realise the nature of his or her mind. A student must receive instructions on Mahamudra meditation directly by a master of this tradition.

Tibetan Buddhism