Vedanta literally means “the end of Vedas” as it refers to the last part of the Vedic texts known as the Upanishads. It renounces all ritualism and expresses the notion of Veda in purely philosophical terms.
The Upanishads, found at the end of each of the ancient Vedas (Rigveda, Yajurveda, Samaveda), are highly philosophical and metaphysical and constitute the whole substance of Vedic wisdom. Veda itself means "Knowing or Knowledge" and hence the meaning of Vedanta can be interpreted as "End of Knowledge" meaning where knowledge ends and higher contemplation begins.
The term Upanishad is derived from upa (near), ni (down) and s(h)ad (to sit), i.e., sitting down near. Groups of pupils sit near the teacher to learn from him the doctrine of various philosophies. This just emphasizes the fact that the study of the Upanishads requires guidance from a teacher as it is highly abstract in nature. As a result, there have been several interpretations of the Upanishads based on the various teachers and a few of them became quite popular based on how much of a mass appeal it had in the intellectual circles. One of the most popular interpretations is the Advaita philosophy.
Advaita Vedanta is the doctrine of non-duality that declares that there is but one reality, that the awareness of the self and the universal awareness are one and that awareness is the only universal truth.
There have been several interpretations of the Upanishads that have brought out this theory of non-duality, the most popular one being the Bhagavad Gita. Bhagavad Gita was created by Veda Vyasa in terms of a philosophical dialog between Krishna and Arjuna in the battlefield of Kurukshetra. The 700 verses of Gita provide this explanation of non-duality in the context of the conflict within Arjuna’s mind and then go on to provide the ultimate self-help textbook.
Adi Shankaracharya formalized the theory of Advaita using the interpretation from the Upanishads and Vedas and the teachings of his own teacher Gaudapada. Sri Shankaracharya defines the fundamental tenet of Advaita Vedanta thus:
brahma satyam jagan mithya
jivo brahmaiva napara
Brahman is the Reality, the universe is an illusion;
the living being is Brahman alone, none else.
Shankaracharya (ca. 800 CE) lived for about 32 years and during that short period consolidated the doctrine of Advaita Vedanta in the whole Indian sub-continent. His principal works include his Bhashyas (commentaries) on the Upanishads, the Bhagavad Gita and the Brahma Sutras. During his time Hinduism was in chaos divided into several sects along with the growing spread of Buddhism and Jainism. He traveled across India to propagate the philosophy of Advaita through debates and discourses and united these different sects by reintroducing the purer form of Vedic thought. He then established four Mathas in four corners of India to serve as hubs for the development Hindu religion especially the philosophy of Advaita. These Mathas - at Sringeri in Karnataka (South), Dwaraka in Gujarat (West), Puri in Orissa (East), and Jyotirmath in Uttarakhand (North) – each associated with a particular Veda and a Mahakavya still continue to (or at least are supposed to!) operate as centers for the development of the Hindu religion . Shankaracharya's greatness is not just in expounding the knowledge, or formalizing the theories but also the way he organized the revival, development and spreading of the ancient Indian philosophies and ideas (broadly classified as the Hindu religion).
Modern age has also seen several proponents of Advaita Vedanta, its core philosophy and its implications. Noteworthy philosophers and thinkers include Sri Ramana Maharshi, Sri Ramakrishna Paramahamsa, Swami Vivekananda, Sri Narayana Guru, Sri Aurobindo, Swami Chinmayananda, etc.