Yoga is an ancient art focussed on development of the body, mind and spirit using harmonized system. Yoga literally means to join, or to unite - here the different context has different meanings like uniting our finite microcosmic individual self with the infinite absolute and pure macrocosmic consciousness. In the same context, yoga is defined as unitive discipline of love/ devotion in Bhagwad Gita, unitive discipline of the kundalini power in kundalini yoga, unitive discipline of sounds that help protect the mind in mantra yoga, unitive discipline of insight in sankhya yoga, unitive discipline of tantras - kundalini based in Tantra yoga, unitive discipline of focussing the mind upon the geometric representations (yantra) in yantra yoga.
Based on the union, yoga has been classified as Jnana Yoga - Union by knowlege, bhakti yoga - union by love and devotion, karma yoga - union by action and service, raja yoga - union by mental mastery and hatha yoga - union by bodily master.
As per the question, I may further add that the history of yoga is divided into following four categories:
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Vedic Yoga - referred to Yogic teachings in vedas - veda means knowledge. 4 Vedas - Rig veda (rig-praise) - collections of hymns that are in praise of a higher power, Yajur-veda (knowledge of sacrifice) - collection of sacrificial formulas used by vedic priests, Sama-veda (knowledge of Chants) - collection of chants accompanying the sacrifices and Atharva-Veda (Knowledge of Atharvan) - It is connected with Atharvan, a famous fire priest who is remembered as having been a master of magical rituals.
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Preclassical Yoga - referred to Ramayana and Mahabharata - This covers an extensive period of approx. 2000 years until the second century. This yoga comprises of many schools whose teachings can be found in Ramayana and Mahabharata.
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Classical Yoga - referred to Astanga or Raja yoga or patanjali's yoga
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Post-classical Yoga - referred to types and schools of yoga that have cropped up after sage Maharshi Patanjali.
