Modern yoga is a physical activity consisting largely of asanas, often connected by flowing sequences called vinyasas, sometimes accompanied by the breathing exercises of pranayama, and usually ending with a period of relaxation or meditation. It is often known simply as yoga, despite the existence of multiple older traditions of yoga within Hinduism where asanas played little or no part, some dating back to the Yoga Sutras, and despite the fact that in no tradition was the practice of asanas central.
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.
Description of an early form of yoga called nirodhayoga (yoga of cessation) is contained in the Mokshadharma section of the 12th chapter (Shanti Parva) of the Mahabharata (third century BCE). Nirodhayoga emphasizes progressive withdrawal from the contents of empirical consciousness such as thoughts, sensations etc. until purusha (Self) is realized. Terms like vichara (subtle reflection), viveka (discrimination) and others which are similar to Patanjali's terminology are mentioned, but not described. There is no uniform goal of yoga mentioned in the Mahabharata. Separation of self from matter, perceiving Brahman everywhere, entering into Brahman etc. are all described as goals of yoga. Samkhya and yoga are conflated together and some verses describe them as being identical. Mokshadharma also describes an early practice of elemental meditation. Mahabharata defines the purpose of yoga as the experience of uniting the individual ātman with the universal Brahman that pervades all things.
Core: Yes. There are yoga poses to target just about every core muscle. Want to tighten those love handles? Then prop yourself up on one arm and do a side plank. To really burn out the middle of your abs, you can do boat pose, in which you balance on your "sit bones" (the bony prominences at the base of your pelvic bones) and hold your legs up in the air.