Physical Yoga (hatha yoga) has existed for thousands of years in an unstructured way until an Indian sage called Patanjali put all the teachings together in a book called the Yoga Sutras. And with that book, yoga became more of an structured practice but only for a few yogis living in remote places.
Yoga had to wait until the beginning of th 20th century, to get formally organised, described and illustrated. That is when yoga travelled outside of India to the West and started becoming popular. A number of famous gurus developed their own way of teaching, adding their personal touch and thereby creating unique yoga styles (although we need to bear in mind that there is only 1 yoga, aiming at uniting the body, the mind and the soul). So here is a quick overview of the most common yoga styles:
Iyengar Yoga:
Created by B.K.S Iyengar in India in the middle of the 20th century.
Highly structured, the most therapeutical kind of yoga there is. It is aimed at opening and aligning the body. Iyengar teachers show the posture, explaining in details how to perform it before students repeat it accordingly. Thanks to the use of yoga props (accessories such as yoga blocks, belts, chairs and so on) it can be practised by anyone: people with severe back pains, missing arm...
It can only be taught by certified Iyengar teachers who went through an extensive training: the main iyengar teachers training takes 3 years and can only be started after 5 years of practice.
Ashtanga Yoga (also known as Mysore Style):
Created by K. Pattabhi Jois in India in the 20th century.
It is based on a structured practice of a fixed sequence of postures. Asthangis momorize and practice the same sequence everyday for years until they can move onto the next sequence (3 sequences in total). During class, each yogi performs a self practice. The teacher is there to assist and adjust postures.
Sivananda Yoga
Founded by Swami Vishnudevananda in the mid 20th century following the teachings of Swami Sivananda.
Swami Vishnudevananda was sent out to the west to teach yoga and share its spiritual teachings. Swami Sivananda redacted a lot of material freely available.
Yoga postures (asanas) have a very important place in this traditional yoga style. It is based on the following: 'Serve. Love. Give. Purify. Meditate. Realize.'
Kundalini Yoga:
Kundali yoga has existed for centuries. The way is is taught today follows the teaching of Yogi Bhajan who was famous in the US in the 1960s and years after. Kundalini yoga taught by Yogi Bhajan is a mix of yoga postures, meditation and breathing excercises aimed at awakening the subtle spiritual energies that lie in the body. The kundalini energy circulates around the 6 chakras before reaching the 7th one located at the top of our head.
Jivamukti Yoga:
A yoga method created by David Life Sharon Gannon in 1984 in the US. They both were disciples of Patthabi Jois.
Is is a vigorous yoga style. It integrates the physical practise together with chanting, meditating, devotion to God as well as non-violence practice (veganism and environment activism).
Bikram Yoga:
Bikram Yoga is a registered trade mark born in the 1970s. It was founded by Bikram Choudhury in the USA.
Bikram yoga is a type of hot yoga practiced in a room at a temperature of 40 °C (104 °F). It consists of a series of 26 fixed hatha yoga postures and 2 breathing excercices. The temperature is said to heat the muscle and help them stretch better. IT also claims to help burn fat quicker.
There are Bikram franchises all over the world.
Vinyasa yoga:
It is a dynamic type of yoga where postures flow from one to the next and are accompanied by the breath. It is highly creative and not as structured as other types of yoga.
Yin Yoga:
It is a type of meditative and slow motion yoga aimed at relaxing both the body and the mind and letting go of tensions. It is practiced in a very "cosy manner" using as many cushions as needed to feel comfortable. The body stretches using its own weight and gravity, without the hands reaching for the feet etc. Breathing has an important role, helping the body release tensions. Yin yogis hold each posture for a good while.
These are only the few main yoga types. There are many many more....