Yoga is one of the biggest contributions India made to the world. From many yoga styles widespread in India we would emphasize Bhakti Yoga, Hatha Yoga, Raja Yoga and Jnana Yoga. Hatha Yoga is one of the most widespread in the United States and Europe as it doesn't places the emphasis on spiritual practices rather on physical exercises.
Today Hatha Yoga is a supplementary fitness system. This particular system of Yoga was introduced by Yogi Sage Swatmarama who lived in the fifteenth century in India. He compiled the doctrine of the Hatha Yoga Pradipika. This doctrine has much in common with the Buddhist tradition especially with the Hinayana (narrow path), the Sahajayana (spontaneous path), Mahayana (great path) and Vajrayana (concerning matters of sexuality). Hatha Yoga is different from Raja Yoga for instance because it focuses on the physical purification that is necessary for the mental purification.
At the same time Raja Yoga deals with the mind first considering its purification necessary to achieve enlightenment and various postures and breath control on which Hatha Yoga is based are considered only a supplementary step. Traditional Hatha Yoga comprises certain moral principles, physical exercises or postures and very important breath control. The philosophy of Hatha Yoga assumes there are opposing energies such as cold and hot, female and male, positive and negative and draws parallels between them.
The key of Hatha Yoga is seeking a balance between opposite energies through various physical postures called "asanas", breath control and meditation. The physical exercises are necessary to prepare the mind for meditation in the pursuit of enlightenment. Hatha yoga is one of the best yoga styles for beginners and that is why it is very popular in the West.
Karma Yoga is also one of the most popular yoga styles. The main principle of Karma Yoga consists in the discipline of action. Karma Yoga is tightly intertwined with Hinduism where the most important thing for a person is the adherence to duty ("dharma") while remaining detached from the reward. By such adherence one can achieve salvation and liberation ("Moksha") by performing his duties in an unselfish manner.
Bhakti Yoga is a popular Indian spiritual practice for which the most important thing is loving devotion (bhakti) to God-creator. Bhakti Yoga is a Hindu practice as there is a difference between purposes of different yoga styles. This difference depends on a religion. For instance in Buddhism there is no concept of God-creator and an individual human-being can himself attain the highest state of the soul becoming equal to God.
The enlightenment is different in Hinduism where an individual can get closer to God-creator by doing spiritual practices. In Bhakti Yoga self-realization can be attained by the instinct emotion of love and redirecting it to the highest pursuit of God. Also there are other yoga styles however in this yoga styles description the most important yoga concepts were listed.