The Upanishads do not abolish sacrifice, but they relocate the point of it. Ritual buys good worlds, and good worlds run out. What ends the cycle is knowledge.
The cycle itself gets its first clear statement here. Rebirth governed by act, karma as moral causation carrying over from life to life, appears in the Brihadaranyaka as something taught privately, almost reluctantly, as if new. From it follows samsara, the round of deaths and births, and moksha, release from it, and those three terms then organise almost everything in Indian religion afterwards, including Buddhist and Jain versions that reject Vedic authority outright.
The positive claim is identity. In the sixth book of the Chandogya, Uddalaka Aruni instructs his son Svetaketu through a sequence of homely demonstrations, salt dissolved in water, the sap in a tree, a banyan seed cut open, and closes each with the formula rendered "you are that", asserting that the finest essence of everything and the boy's own self are one thing. The Brihadaranyaka approaches from the other side, with Yajnavalkya defining the self only by denial, "not this, not this", because anything specified would be an object and the self is what does the specifying. The Katha stages the question as a boy named Naciketa extracting from Death himself the answer about what survives.
None of this is a system, and the schools that later built systems read the same sentences to opposite conclusions. Shankara took identity strictly and argued that plurality is finally unreal; Ramanuja read the same texts as describing a real world and real souls forming the body of a personal God; Madhva read them as asserting difference. All three wrote commentaries on the Upanishads, the Brahma Sutras and the Bhagavad Gita, the set known as the prasthanatrayi, because in Vedanta an argument is only legitimate if it can be shown to be exegesis.