During the Gupta period (4th to 5th centuries), a movement of northern Mahāyāna Buddhism termed Yogācāra began to be systematized with the writings of the Buddhist scholars Asanga and Vasubandhu. Yogācāra Buddhism received the name as it provided a "yoga," a systematic framework for engaging in the practices that lead through the path of the bodhisattva towards awakening and full Buddhahood. Its teachings can be found in the comprehensive and encyclopedic work, the Yogācārabhūmi-Śāstra (Treatise on the Foundation for Yoga Practitioners), which was also translated into Tibetan and Chinese and thus exerted a profound influence on the East Asian Buddhist and Tibetan Buddhist traditions. According to Mallinson and Singleton, the study of Yogācāra Buddhism is essential for the understanding of yoga's early history, and its teachings influenced the text of the Pātañjalayogaśāstra.
The Bhakti movement was a development in medieval Hinduism which advocated the concept of a personal God (or "Supreme Personality of Godhead"). The movement was initiated by the Alvars of South India in the 6th to 9th centuries, and it started gaining influence throughout India by the 12th to 15th centuries. Shaiva and Vaishnava bhakti traditions integrated aspects of Yoga Sutras, such as the practical meditative exercises, with devotion. Bhagavata Purana elucidates the practice of a form of yoga called viraha (separation) bhakti. Viraha bhakti emphasizes one pointed concentration on Krishna.
Theosophists including Madame Blavatsky also had a large influence on the Western public's view of Yoga. Esoteric views current at the end of the 19th century provided a further basis for the reception of Vedanta and of Yoga with its theory and practice of correspondence between the spiritual and the physical. The reception of Yoga and of Vedanta thus entwined with each other and with the (mostly Neoplatonism-based) currents of religious and philosophical reform and transformation throughout the 19th and early 20th centuries. Mircea Eliade brought a new element into the reception of Yoga with the strong emphasis on Tantric Yoga in his seminal book: Yoga: Immortality and Freedom. With the introduction of the Tantra traditions and philosophy of Yoga, the conception of the "transcendent" to be attained by Yogic practice shifted from experiencing the "transcendent" ("Atman-Brahman" in Advaitic theory) in the mind to the body itself.
Tantra is a range of esoteric traditions that began to arise in India no later than the 5th century CE.[note 17] George Samuel states, "Tantra" is a contested term, but may be considered as a school whose practices appeared in mostly complete form in Buddhist and Hindu texts by about 10th century CE. Tantric yoga developed complex visualizations which included meditation on the body as a microcosm of the cosmos. They included also the use of mantras, pranayama, and the manipulation of the subtle body, including its nadis and cakras. These teachings on cakras and Kundalini would become central to later forms of Indian Yoga.
Equipment required? No. You don't need any equipment because you'll rely on your own body weight for resistance. But you'll probably want to use a yoga mat to keep you from sliding around in standing poses, and to cushion you while in seated and lying positions. Other, optional equipment includes a yoga ball for balance, a yoga block or two, and straps to help you reach for your feet or link your hands behind your back.