This from the Encyclopedia Britannica (on-line)
With the last component of the Vedas, the philosophically oriented and esoteric texts known as the Upanishads (traditionally “sitting near a teacher” but originally understood as “connection” or “equivalence”), Vedic ritualism and the doctrine of the interconnectedness of separate phenomena were superseded by a new emphasis on knowledge alone—primarily knowledge of the ultimate identity of all phenomena, which merely appeared to be separate. The beginnings of philosophy and mysticism in Indian religious history occurred during the period of the compilation of the Upanishads, roughly between 700 and 500 bce. Historically, the most important of the Upanishads are the two oldest, the Brihadaranyaka (“Great Forest Text”; c. 10th–5th century bce) and the Chandogya (pertaining to the Chandogas, priests who intone hymns at sacrifices), both of which are compilations that record the traditions of sages (rishis) of the period—notably Yajnavalkya, who was a pioneer of new religious ideas.
The Upanishads reveal the desire to obtain the mystical knowledge that ensures freedom from “re-death” (punarmrityu), or birth and death in a new existence. Throughout the later Vedic period, the idea that the world of heaven is not the end of existence—and that even in heaven death is inevitable—became increasingly common. Vedic thinkers became concerned about the impermanence of religious merit and its loss in the hereafter, as well as about the transience of any form of existence after death—an existence that would culminate in re-death. The means of escaping and conquering death devised in the Brahmanas were of a ritual nature, but one of the oldest Upanishads, the Brihadaranyaka Upanishad, emphasizes the knowledge of the cosmic connection underlying ritual. When the doctrine of the identity of atman (the self) and brahman (the Absolute) was established in the Upanishads, those sages who were inclined to meditative thought substituted the true knowledge of the self and the realization of this identity for the ritual method.
This theme of the quest for a supreme unifying truth, for the reality underlying existence, is exemplified in the question posed by the seeker in the Mundaka Upanishad: “What is it that, by being known, all else becomes known?” What is sought is an experiential knowledge that is different from the “lower” knowledge that can be conceptualized and articulated by human beings. Thus, the supreme truth is understood as ineffable. The Taittiriya Upanishad says that brahman is this ineffable truth; brahman is also truth (satya), knowledge (jnana), infinity (ananta), consciousness (chit), and bliss (ananda). Other Upanishads describe brahman as the hidden, inner controller of the human soul. The experiential knowledge of the relationship between the human soul (atman) and the supreme being (brahman) is said to bring an end to the cycle of birth, death, and rebirth. To know brahman is to know all; in knowing brahman, one achieves a transcendental consciousness that comprehends, in some measure, the unity of the universe and the deep connection between the soul and brahman.
In subsequent centuries the main theories concerned with the divine essence underlying the world were harmonized and synthetically combined. The tendency of these theories was to extol one god as the supreme lord and originator (Ishvara)—at once Purusha and Prajapati and brahman and the self of all beings. For those who worshipped him, he was the goal of identificatory meditation, which leads to complete cessation of phenomenal existence and becomes the refuge of those who seek eternal peace. The Advaita Vedanta philosopher and theologian Shankara (8th century ce) exercised enormous influence on subsequent Hindu thinking through his elegant synthesis of the nontheistic and theistic aspects of Upanishadic teaching. In his commentaries on several of the Upanishads, he distinguished between nirguna brahman (without attributes) and saguna brahman (with attributes). His was a monistic teaching that stressed that saguna brahman was a lesser, temporary form of nirguna brahman. He taught also that the self (atman) is identical with nirguna brahman and that through knowledge of this unity the cycle of rebirth can be broken.
The Upanishads were composed during a time of much social, political, and economic upheaval. Rural tribal society was disappearing, and the adjustments of the people to urban living under a monarchy probably provoked many psychological and religious responses. During this period many groups of mystics, world renouncers, and forest dwellers appeared in India, among whom were the authors of the Upanishads. The most important practices and doctrines of these world renouncers included asceticism and the concept of rebirth, or transmigration.
The Rigveda contains few examples of asceticism, except among the “silent ones” (munis). The Atharvaveda describes another class of religious adepts, or specialists, the vratyas, particularly associated with the region of Magadha (west-central Bihar). The vratya was a wandering hierophant (one who manifested the holy) who remained outside the system of Vedic religion. He practiced flagellation and other forms of self-mortification and traveled from place to place in a bullock cart with an apprentice and with a woman who appears to have engaged in ritual prostitution. The Brahmans sought to bring the vratyas into the Vedic system by special conversion rituals, and it may be that the vratyas introduced their own beliefs and practices into Vedic religion. At the same time, the more-complex sacrifices of the later Vedic period demanded purificatory rituals, such as fasting and vigil, as part of the preparations for the ceremony. Thus, there was a growing tendency toward the mortification of the flesh.
The origin and development of the belief in transmigration of souls are very obscure. A few passages suggest that this doctrine was known even in the days of the Rigveda, and the Brahmanas often refer to doctrines of re-death and rebirth, but it was first clearly propounded in the earliest Upanishad—the Brihadaranyka. There it is stated that the soul of a Vedic sacrificer returns to earth and is reborn in human or animal form. This doctrine of samsara (reincarnation) is attributed to the sage Uddalaka Aruni, who is said to have learned it from a Kshatriya chief. In the same text, the doctrine of karma (“actions”), according to which the soul achieves a happy or unhappy rebirth according to its works in the previous life, occurs for the first time and is attributed to the theologian Yajnavalkya. Both doctrines seem to have been new, circulating among small groups of ascetics who were disinclined to make them public, perhaps for fear of the orthodox priests. These doctrines must have spread rapidly, for they appear in the later Upanishads and in the earliest Buddhist and Jain scriptures.