Power Yoga
Power yoga is a derivative of flow or astanga yoga. It is a continuous sequence of asanas with an emphasis on developing awareness and control of the breath. This leads to increased will power, clarity of thought, and self confidence.

Asanas are not thought to be invented by a human but are the gift of Lord Siva, who originally described 8,400,000 poses. Of this knowledge, only a scant few remain.
Power yoga is designed to improve the health of the spine, posture and lower back as well as to balance and strengthen the nervous system and focus the mind.

When you improve the way energy flows in your body, you change the way your energy interacts with other people’s energy. You change the way you think and feel about yourself, and the way that others think and feel about you.

Kundalini yoga
Kundalini yoga is a practice for mechanically rewiring the way energy moves through your body, through your chakras, and through your aura.
This is accomplished through intensive kriyas (activities/exercises) which are combinations of asanas (yoga postures), pranayama (breathing techniques), mudras (gestures), bandas (energy locks), and mantras (sacred sound vibrations).

It is considered a very fast acting yoga. It strongly conditions and strengthens the nervous system. It is a yoga for modern spiritual warriors.
The origins of Kundalini yoga are ancient, said to be originated by Kartikeya, son of Lord Siva. They are secrets, only talked about recently. The full essence of it remains hidden. Preliminary descriptions of it can be found in the Gherad Samhita, Siva Samhita, and Kundalini Upanishad.

Slow Deep & Restorative Yoga
Slow deep poses help relieve the effects of chronic stress in several ways. First, the use of props provides a supportive environment for total relaxation. As well as the use of gravity for developing the experience of surrender.
Second, each slow deep sequence is designed to move the spine in all directions. These movements illustrate the age-old wisdom of yoga that teaches well-being is enhanced by a healthy spine. Some of the slow deep stretch poses are backbends, while others are forward bends. Additional poses gently twist the column both left and right.
Third, a slow deep restorative practice usually includes an inverted pose, which reverses the effects of gravity. This can be as simple as putting the legs on a bolster or pillow, but the effects are quite dramatic. Because we stand or sit most of the day, blood and lymph fluid accumulate in the lower extremities. By changing the relationship of the legs to gravity, fluids are returned to the upper body and heart function is enhanced.
Psychobiologist and yoga teacher Roger Cole, Ph.D., consultant to the University of California, San Diego, in sleep research and biological rhythms, has done preliminary research on the effects of inverted poses. He found that they dramatically alter hormone levels, thus reducing brain arousal, blood pressure, and fluid retention. He attributes these benefits to a slowing of the heart rate and dilation of the blood vessels in the upper body that comes from reversing the effects of gravity.
Fourth, restorative yoga alternately stimulates and soothes the organs. For example, by closing the abdomen with a forward bend and then opening it with a backbend, the abdominal organs are squeezed, forcing the blood out, and then opened, so that fresh blood returns to soak the organs. With this movement of blood comes the enhanced exchange of oxygen and waste products across the cell membrane
Finally, yoga teaches that the body is permeated with energy. Prana, the masculine energy, resides above the diaphragm, moves upward, and controls respiration and heart rate. Apana, the feminine energy, resides below the diaphragm, moves downward, and controls the function of the abdominal organs. Atma yoga balances these two aspects of energy so that the practitioner is neither overstimulated nor depleted.
All of this is of course magnified by the use of breath control, particularly by extending the exhalation.