Pranayama
We have studied the art of pranayama with real understanding with Srivatsa Ramaswami
who studied for 33 years with T. Krishnamacharya.
Ramaswami is the student who stayed the longest with T. Krishnamacharya.

II.52. Through the practice of Pranayama, the veil of tamas (heaviness; darkness) which covers the clarity of the mind, is removed.
— Yoga Sutra Patanjali
Subtlety
The fourth branch of Ashtanga Yoga is Pranayama.
PRANA means vital energy or cosmic energy.
YAMA means to lengthen or restrict.
This term is usually translated as "breath control" or "breath control" while it means " develop awareness of the breath".
This consciousness produces a subtle purification of the physical body (the five elements) and of the Tanmatras (the subtle body). These in turn affect Manas (the emotional or conditioned mind), allowing the spirit to have upward movement. Whereas if control takes over, unfortunately, this process reinforces the downward movement of Ahamkara (principle of individuality) and Manas because it accentuates the feeling of being "the doer of one's actions" or the feeling of “I”.
Pranayama exercises allow to develop the respiratory capacities and an improvement of the energy consciousness, and to no longer be influenced by the mind. It is a step towards meditation.
Advantages
Asanas, bandhas and mudras emphasize the importance of keeping the muscles and nadis of the lower part (mula) of the body in good tone. According to yogic theory, many important nadis are located in the anal and pelvic region, and therefore it is repeatedly emphasized that one keeps this area in good condition. In addition, it is the area of the sex glands (prostate, uterus, ovaries), and good muscle tone is particularly essential for proper functioning. Without these asanas, bandhas and mudras, these areas are never exercised.
The 3 main Bandhas (locks) - Mula Bandha - Uddiyana Bandha - Jalandhara Bandha. These are energy points that engaged allow the circulation and channeling of energy. Prana is directed by currents called Vayus, 5 in number, which dissipate energy upwards and downwards, the bandhas make it possible to conserve this energy so that it does not dissipate. Without the activation of these bandhas in the breathing exercises, there could be harmful effects on the energy of the practitioner, that is why it is important to practice the asanas in order to have commitment and a flexible column.
Pranayama reduces guna tamas (physical and mental inertia) and, together with asana practice, helps cleanse the system of rajas. The result is that you become very sattvic - the ideal condition for the rewarding process of meditation.
The practitioner can obtain some extraordinary influences on his own physiological functions. The basic factor of yoga is breathing. Respiratory function can be influenced more easily than any other vital function, and the yogi uses it as the first step to influence the nervous system.
Pranayama has several physical benefits. It expands the chest, improves vital capacity and helps to slowly overcome several diseases such as bronchial asthma, shortness of breath and irregular breathing. Along with bandhas and mudras, it improves blood circulation to and within the heart.
Pranayama has physiological benefits. Respiratory function is both voluntary and involuntary. Normally, our breathing is shallow and involuntary. In pranayama, a deliberate attempt is made to bring the breath under greater voluntary control, thereby bringing many other involuntary conditions of the body and mind under voluntary control. The mind is trained and adapted to follow the breath and therefore attain the capacity of Ekagra (the 4th state of focus, stable, effortless concentration), which is essential for all other mental and spiritual realizations.

Yogic breathing exercises
● Kapalabhati
● Bastrika
● Nadi Shodhana / Anuloma Viloma
● Sitali et Sitkari Pranayama
● Surya Bhedana Pranayama
● Chandra Bhedana Pranayama
● Ujjayi Pranayama
● Anuloma Ujjayi Pranayama
● Pratiloma Ujjayi Pranayama
● Viloma Ujjayi Pranayama
● Mantra Pranayama
● Bhramari Pranayama
II.53. Pranayama also makes the mind fit for Dharana (supporting an idea).
Dharana (discernment - concentration) this term is appropriate only when we realize the difference between Manas (the emotional or conditioned mind) and Buddhi (individual, sensitive intellect).
— Yoga Sutra Patanjali
"Regulate the breath, be happy, connect the spirit to the source in your heart"
— T. Krishnamacharya