The Upanishads get their name from a Hindu phrase meaning something like, "By sitting near." This is a reference to the texts' esoteric nature, that this is what was learned from the teacher by sitting nearest to him. The Upanishads are an expression of the intimate discoveries of early masters of meditation and philosophy, hundreds of years before the Buddha lived on earth.
Although there are variations among the eastern mystic religions and philosophies, the Upanishads are a clear indication of their common ancestry, demonstrating what the religions have most in common—a distrust of the visible reality, a thirst for true enlightenment, and an uncompromising self-awareness and self-mastery as the path to transcendence.
Major analytical themes among the earliest Upanishads include knowing one's soul through introspective meditation and the analysis of one's desires. The soul is referred to as Atman and does not necessarily correspond to one's emotional thought-life, but rather one's core sense of being. In fact, a major distinction can be drawn here between eastern and western schools of thought, because whereas the western world tends to view the soul as the part of the self that distinguishes one from the many through a process of differentiation and choice, the Upanishads seem to be arguing that the true Atman is not different from person to person, and therefore, the path to ascension must include the discovery of 'oneness,' both with nature itself and with all living beings.
The ultimate goal of this pursuit in one's Atman is to discover Brahman, which is the true reality, beyond what this current time-oriented reality shows us. This is where Karma comes in to play. Upon meditating on the nature of the passage of time and on the nature of causality, the practicer of this ancient way wants to understand karmic energy so that it can eventually be overcome. The goal of correctly practiced meditation is the liberation of the soul (Mukti), which in some traditions results in the spontaneous transcendence of this reality, meaning that one might actually vanish to become reabsorbed into the energy of the universe, or in other traditions, Mukti might mean mastery over nature, the ability to perform miracles, the ability to practice divination, the ability to defy the laws of physics, etc.
Another major analytical aspect of the Upanishads concerns reincarnation. There is some dispute among eastern thought as to the nature of reincarnation, but essentially, its function is to reallocate the soul into higher or lower castes of existence upon one's death, depending on their Karma. The goal, then, of a practicer of this way is to eventually rise through the ranks of existence until finally in one of their many lives, they can exit reality through nirvana instead of karmic reincarnation.
Correctly understood, this eastern mode of thought serves as a complement to the positivistic tradition of the west, and many in Christian mysticism and Islamic mysticism (particularly Sufi mysticism) have learned to see the teachings of the Upanishads in harmony with other major world religions.