Shadanga Yoga

prAnAyAma iti prAnasya sthirata recaka pUraka kumbhaka samghattakarana catvari prAnAyAma laksanAni
  Pranayama is the stability of the breathing. The exhalation, the inhalation, the holding of breath and their combination; these are the four features of breath control.

2.35 Siddha siddhAnta paddhatiH
of GorakshanAtha

Breathing, Pranayama, Mastery of Life Force.
Breathing connects our inner core to the outer world. It is a bridge between the conscious and the subconscious, the connection between body (the past) and mind (the future), solely the breath abides in this moment, in the here and now.

Breath is a measure of time. A balanced healthy person breathes 21,600 times in 24 hours. 10800 of these breaths are of a solar detoxifying and invigorating nature (related to right nasal opening) and 10800 breath (related to the left nasal opening) are of a lunar, soothing and nourishing nature.
 

Breathing should be steady, deep and uncoerced and the exhalation should empty the lungs as completely as possible. This is the ideal but because of stress, rush and traumatic experiences this balance is unsettled.

Today there is a tendency to breathe way too fast and too shallow, about 18-20 Breath cycles per minute has become the norm. That way only 1/8 of the lung capacity is utilised and only 1/6 of the air is exchanged. When the body is exerted it demands more oxygen and the exchange of air is tenfold. Using pranayama we harmonise and stabilise the breathing cycle.

Breath is the link between voluntary and involuntary activity. Holding the breath is partly a conscious activity, for instance during an effort to concentrate or listen attentively, and partly a subconscious one, for instance during moments of fear or lack of trust.
But it is not solely the breathing that stops or is irregular. Breathing patterns influence the circulation of lymphatic fluid which is cleaning the organism of impurities and toxins, and is activated by ample supply of oxygen. Inefficient breathing restricts the cellular regeneration. Wrong breathing is hurrying the ageing process. Muscles that relax during deep breathing tense, shrink and harden because of shallow breathing. Blockages develop.
Once a muscle is tense there is little chance to provide it with fresh energy. Pain restricts the breath and causes one to assume a relieving posture to avoid still further pain. While in the relieving posture breath cannot penetrate into the core of the tension and is unable to release it. A human in pain will breathe shallow, he is in a bad mood and tensions aggravate. This state of irritation and edginess adds even more muscular tension. It is crucial to break this vicious cycle. Becoming aware of the interconnectedness of mind, body and breath is the first step.

When the mind receives an impression the brain analyses it and orders the nervous system to keep certain muscles tense and others relaxed. To become balanced and flexible the mind should not be too sensitive to outward impressions. If the mind is at ease the breath flows deep and smooth and the muscles are supplied with fresh blood and new energy. The body is relaxing.
The simplest way to quieten the mind is taking a deep breath. By learning to control the breath the mind will not readily surrender to outward impressions. We can complete tasks with equanimity and full command over all our abilities.

With the practice of pranayama we can deepen our breathing, and attain mastery over breathing. This has to be achieved with ease and with individual guidance. There should be no coercion in breathing.

The Application of Pranayama during the Practice of Immersion (dhyana)
It is written in the "Goraksha Sataka", a text of the middle ages stemming from the nath-siddha tradition, attributed to Gorakshanatha, the great yogi and founder of Hatha Yoga:

„Whosoever has brought his mental activities to rest, has also brought his breathing to rest. When the breathing stops the mind is stopped as well. Like milk and water (when they are mixed) become one, in the same way breath and mind unite. As the breathing behaves, the mind will  behave similarly. When the one is mastered the other follows in its track. Mind masters the sense impressions and desires. Breath masters the mind. That which masters the breath is dissolution (laya) and dissolution is based on sound (nada).“

Prana denotes the breath as well as the life force, this prana moves in subtle channels called nadis, the practice of pranayama can purify and open these channels. A yogi can, by means of his breath, control his mind as well as his gross and subtle body. This subtle body (sukshma sharira) consists of the life forces or winds (pranavayu), the dots, drops or light points (bindu) that flow in the nadis and the eight mental building blocks (puryastaka)
Some of the meditative absorptions called „Laya“ (dissolution), that are able, according to the „Goraksha Sataka“, to master the breath, utilise sound „nada“ to achieve this dissolution. In the Yoga teachings the practice of mantra ultimately serves the purpose of laya. Among all the mantras it is the practice of  „Om“ and the Prasada Mantra „hamsah“ that are primarly used to achieve dissolution based on the principle of sound, „nada“.
Pranayama, connected with language in the form of mantras and  meditation on primordial sound and its natural intent, are effective methods of Hatha Yoga. They are based on pranayama and deepen its scope. Meditation, language and sound are utilised to master breathing as well as life force. The inseparability of opposites, like that between subject and object and other profound experiences and realisations can that way be actualized. The accompanying illustration depicts the incremental rising (uccharana) and rarefication of the life energy (prana) and sound (nada) in the yogic subtle body and beyond it into space (kha, akasha)