Breath Control or Prāṇāyāma

School of Yoga explains prāṇāyāma. 

In classical Yoga, prāṇāyāma means controlling the breathing process. Here, prāṇāyāma means prāṇa = motility or that which enables life + yama = control. So, prāṇāyāma is actually control of motility (prāṇa) using breath as a tool. Prāṇāyāma is a natural progression of āsana. Consequently, the various techniques of prāṇāyāma are generally taught with āsana. School of Yoga considers proper practice of prāṇāyāma to be as important as practice of āsana.

Classical yoga defines prāṇāyāma or breath control

The Hatha Yoga Pradeepika has a complete chapter on prāṇāyāma. 

Chapter 2 of Hatha Yoga Pradeepika says:

1. Once a yogi has perfected āsana, he should maintain a beneficial and moderate diet and practice prāṇāyāma as instructed by his Guru.
2. When the breath is disturbed, the mind becomes disturbed. When the breath is still, so is the mind.
3. For as long as there is prāṇa in the body, there is life. Death occurs when prāṇa leaves the body, hence the need to restrain it.
4. Owing to impurities in the nādis, the prāṇa does not pass through the middle channel. So how can one achieve the state of the precious gem (unmani)? How does one achieve siddhi?
5. When all the nādi’s are cleansed, then the yogi is able to restrain the breath.

This section of School of Yoga addresses all major aspects of prāṇāyāma.